Koushil Sreenath

Ashish Kumar, Zhongyu Li, Jun Zeng et al. · berkeley

Recent advances in legged locomotion have enabled quadrupeds to walk on challenging terrains. However, bipedal robots are inherently more unstable and hence it's harder to design walking controllers for them. In this work, we leverage recent advances in rapid adaptation for locomotion control, and extend them to work on bipedal robots. Similar to existing works, we start with a base policy which produces actions while taking as input an estimated extrinsics vector from an adaptation module. This extrinsics vector contains information about the environment and enables the walking controller to rapidly adapt online. However, the extrinsics estimator could be imperfect, which might lead to poor performance of the base policy which expects a perfect estimator. In this paper, we propose A-RMA (Adapting RMA), which additionally adapts the base policy for the imperfect extrinsics estimator by finetuning it using model-free RL. We demonstrate that A-RMA outperforms a number of RL-based baseline controllers and model-based controllers in simulation, and show zero-shot deployment of a single A-RMA policy to enable a bipedal robot, Cassie, to walk in a variety of different scenarios in the real world beyond what it has seen during training. Videos and results at https://ashish-kmr.github.io/a-rma/

Gilbert Feng, Hongbo Zhang, Zhongyu Li et al. · berkeley

Recent years have seen a surge in commercially-available and affordable quadrupedal robots, with many of these platforms being actively used in research and industry. As the availability of legged robots grows, so does the need for controllers that enable these robots to perform useful skills. However, most learning-based frameworks for controller development focus on training robot-specific controllers, a process that needs to be repeated for every new robot. In this work, we introduce a framework for training generalized locomotion (GenLoco) controllers for quadrupedal robots. Our framework synthesizes general-purpose locomotion controllers that can be deployed on a large variety of quadrupedal robots with similar morphologies. We present a simple but effective morphology randomization method that procedurally generates a diverse set of simulated robots for training. We show that by training a controller on this large set of simulated robots, our models acquire more general control strategies that can be directly transferred to novel simulated and real-world robots with diverse morphologies, which were not observed during training.

Xiaoyu Huang, Zhongyu Li, Yanzhen Xiang et al. · berkeley

We present a reinforcement learning (RL) framework that enables quadrupedal robots to perform soccer goalkeeping tasks in the real world. Soccer goalkeeping using quadrupeds is a challenging problem, that combines highly dynamic locomotion with precise and fast non-prehensile object (ball) manipulation. The robot needs to react to and intercept a potentially flying ball using dynamic locomotion maneuvers in a very short amount of time, usually less than one second. In this paper, we propose to address this problem using a hierarchical model-free RL framework. The first component of the framework contains multiple control policies for distinct locomotion skills, which can be used to cover different regions of the goal. Each control policy enables the robot to track random parametric end-effector trajectories while performing one specific locomotion skill, such as jump, dive, and sidestep. These skills are then utilized by the second part of the framework which is a high-level planner to determine a desired skill and end-effector trajectory in order to intercept a ball flying to different regions of the goal. We deploy the proposed framework on a Mini Cheetah quadrupedal robot and demonstrate the effectiveness of our framework for various agile interceptions of a fast-moving ball in the real world.

Chenyu Yang, Guo Ning Sue, Zhongyu Li et al. · berkeley

This paper tackles the problem of robots collaboratively towing a load with cables to a specified goal location while avoiding collisions in real time. The introduction of cables (as opposed to rigid links) enables the robotic team to travel through narrow spaces by changing its intrinsic dimensions through slack/taut switches of the cable. However, this is a challenging problem because of the hybrid mode switches and the dynamical coupling among multiple robots and the load. Previous attempts at addressing such a problem were performed offline and do not consider avoiding obstacles online. In this paper, we introduce a cascaded planning scheme with a parallelized centralized trajectory optimization that deals with hybrid mode switches. We additionally develop a set of decentralized planners per robot, which enables our approach to solve the problem of collaborative load manipulation online. We develop and demonstrate one of the first collaborative autonomy framework that is able to move a cable-towed load, which is too heavy to move by a single robot, through narrow spaces with real-time feedback and reactive planning in experiments.

Zhongyu Li, Jun Zeng, Akshay Thirugnanam et al. · berkeley

Bridging model-based safety and model-free reinforcement learning (RL) for dynamic robots is appealing since model-based methods are able to provide formal safety guarantees, while RL-based methods are able to exploit the robot agility by learning from the full-order system dynamics. However, current approaches to tackle this problem are mostly restricted to simple systems. In this paper, we propose a new method to combine model-based safety with model-free reinforcement learning by explicitly finding a low-dimensional model of the system controlled by a RL policy and applying stability and safety guarantees on that simple model. We use a complex bipedal robot Cassie, which is a high dimensional nonlinear system with hybrid dynamics and underactuation, and its RL-based walking controller as an example. We show that a low-dimensional dynamical model is sufficient to capture the dynamics of the closed-loop system. We demonstrate that this model is linear, asymptotically stable, and is decoupled across control input in all dimensions. We further exemplify that such linearity exists even when using different RL control policies. Such results point out an interesting direction to understand the relationship between RL and optimal control: whether RL tends to linearize the nonlinear system during training in some cases. Furthermore, we illustrate that the found linear model is able to provide guarantees by safety-critical optimal control framework, e.g., Model Predictive Control with Control Barrier Functions, on an example of autonomous navigation using Cassie while taking advantage of the agility provided by the RL-based controller.

Aaron D. Ames, Samuel Coogan, Magnus Egerstedt et al.

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

Lizhi Yang, Zhongyu Li, Jun Zeng et al. · berkeley

In this paper, we propose a multi-domain control parameter learning framework that combines Bayesian Optimization (BO) and Hybrid Zero Dynamics (HZD) for locomotion control of bipedal robots. We leverage BO to learn the control parameters used in the HZD-based controller. The learning process is firstly deployed in simulation to optimize different control parameters for a large repertoire of gaits. Next, to tackle the discrepancy between the simulation and the real world, the learning process is applied on the physical robot to learn for corrections to the control parameters learned in simulation while also respecting a safety constraint for gait stability. This method empowers an efficient sim-to-real transition with a small number of samples in the real world, and does not require a valid controller to initialize the training in simulation. Our proposed learning framework is experimentally deployed and validated on a bipedal robot Cassie to perform versatile locomotion skills with improved performance on smoothness of walking gaits and reduction of steady-state tracking errors.

Siheng Zhao, Yuanhang Zhang, Ziqi Lu et al.

Humanoid robots hold great promise for operating in human-centered environments, yet ladder climbing remains one of the most challenging tasks due to sparse footholds and handholds, complex whole-body coordination, and sensitivity to perception and control errors. We present \textbf{LadderMan}, a unified system that enables humanoid robots to robustly climb diverse ladders and perform manipulation under such constrained conditions. Our climbing policy is built on a scalable two-stage learning pipeline, where we use hybrid motion tracking to learn multiple climbing experts from a single reference motion, and distill these experts into a unified depth-based visuomotor climbing policy via hybrid imitation and reinforcement learning. To enable real-world deployment, we leverage vision foundation models to bridge the sim-to-real gap in depth perception. Building on the learned climbing policy, we further train a separate manipulation policy using a dual-agent formulation, allowing stable on-ladder manipulation via teleoperation. Experiments demonstrate that LadderMan achieves robust ladder climbing across a wide range of geometries, successfully transfers to real-world hardware in a zero-shot manner, and supports various manipulation tasks under challenging ladder constraints. Video results are available at https://ladderman-robot.github.io .

Ilija Radosavovic, Tete Xiao, Bike Zhang et al.

Humanoid robots that can autonomously operate in diverse environments have the potential to help address labour shortages in factories, assist elderly at homes, and colonize new planets. While classical controllers for humanoid robots have shown impressive results in a number of settings, they are challenging to generalize and adapt to new environments. Here, we present a fully learning-based approach for real-world humanoid locomotion. Our controller is a causal transformer that takes the history of proprioceptive observations and actions as input and predicts the next action. We hypothesize that the observation-action history contains useful information about the world that a powerful transformer model can use to adapt its behavior in-context, without updating its weights. We train our model with large-scale model-free reinforcement learning on an ensemble of randomized environments in simulation and deploy it to the real world zero-shot. Our controller can walk over various outdoor terrains, is robust to external disturbances, and can adapt in context.

Yandong Ji, Zhongyu Li, Yinan Sun et al.

We address the problem of enabling quadrupedal robots to perform precise shooting skills in the real world using reinforcement learning. Developing algorithms to enable a legged robot to shoot a soccer ball to a given target is a challenging problem that combines robot motion control and planning into one task. To solve this problem, we need to consider the dynamics limitation and motion stability during the control of a dynamic legged robot. Moreover, we need to consider motion planning to shoot the hard-to-model deformable ball rolling on the ground with uncertain friction to a desired location. In this paper, we propose a hierarchical framework that leverages deep reinforcement learning to train (a) a robust motion control policy that can track arbitrary motions and (b) a planning policy to decide the desired kicking motion to shoot a soccer ball to a target. We deploy the proposed framework on an A1 quadrupedal robot and enable it to accurately shoot the ball to random targets in the real world.

Zhongyu Li, Xue Bin Peng, Pieter Abbeel et al.

This work aims to push the limits of agility for bipedal robots by enabling a torque-controlled bipedal robot to perform robust and versatile dynamic jumps in the real world. We present a reinforcement learning framework for training a robot to accomplish a large variety of jumping tasks, such as jumping to different locations and directions. To improve performance on these challenging tasks, we develop a new policy structure that encodes the robot's long-term input/output (I/O) history while also providing direct access to a short-term I/O history. In order to train a versatile jumping policy, we utilize a multi-stage training scheme that includes different training stages for different objectives. After multi-stage training, the policy can be directly transferred to a real bipedal Cassie robot. Training on different tasks and exploring more diverse scenarios lead to highly robust policies that can exploit the diverse set of learned maneuvers to recover from perturbations or poor landings during real-world deployment. Such robustness in the proposed policy enables Cassie to succeed in completing a variety of challenging jump tasks in the real world, such as standing long jumps, jumping onto elevated platforms, and multi-axes jumps.

Akshay Thirugnanam, Koushil Sreenath

In this paper, we discuss an efficient algorithm for computing the growth distance between two compact convex sets with representable support functions. The growth distance between two sets is the minimum scaling factor such that the sets intersect when scaled about some center points. Unlike the minimum distance between sets, the growth distance provides a unified measure for set intersection and separation. We first reduce the growth distance problem to an equivalent ray intersection problem on the Minkowski difference set. Then, we propose an algorithm to solve the ray intersection problem by iteratively constructing inner and outer polyhedral approximations of the Minkowski difference set. We show that our algorithm satisfies several key properties, such as primal and dual feasibility and monotone convergence. We provide extensive benchmark results for our algorithm and show that our open-source implementation achieves state-of-the-art performance across a wide variety of convex sets. Finally, we demonstrate robotics applications of our algorithm in motion planning and rigid-body simulation.

Yuanchen Ju, Yongyuan Liang, Yen-Jen Wang et al.

Mobile manipulators in households must both navigate and manipulate. This requires a compact, semantically rich scene representation that captures where objects are, how they function, and which parts are actionable. Scene graphs are a natural choice, yet prior work often separates spatial and functional relations, treats scenes as static snapshots without object states or temporal updates, and overlooks information most relevant for accomplishing the current task. To address these limitations, we introduce MomaGraph, a unified scene representation for embodied agents that integrates spatial-functional relationships and part-level interactive elements. However, advancing such a representation requires both suitable data and rigorous evaluation, which have been largely missing. We thus contribute MomaGraph-Scenes, the first large-scale dataset of richly annotated, task-driven scene graphs in household environments, along with MomaGraph-Bench, a systematic evaluation suite spanning six reasoning capabilities from high-level planning to fine-grained scene understanding. Built upon this foundation, we further develop MomaGraph-R1, a 7B vision-language model trained with reinforcement learning on MomaGraph-Scenes. MomaGraph-R1 predicts task-oriented scene graphs and serves as a zero-shot task planner under a Graph-then-Plan framework. Extensive experiments demonstrate that our model achieves state-of-the-art results among open-source models, reaching 71.6% accuracy on the benchmark (+11.4% over the best baseline), while generalizing across public benchmarks and transferring effectively to real-robot experiments.

Yen-Jen Wang, Bike Zhang, Jianyu Chen et al.

Large language models (LLMs) pre-trained on vast internet-scale data have showcased remarkable capabilities across diverse domains. Recently, there has been escalating interest in deploying LLMs for robotics, aiming to harness the power of foundation models in real-world settings. However, this approach faces significant challenges, particularly in grounding these models in the physical world and in generating dynamic robot motions. To address these issues, we introduce a novel paradigm in which we use few-shot prompts collected from the physical environment, enabling the LLM to autoregressively generate low-level control commands for robots without task-specific fine-tuning. Experiments across various robots and environments validate that our method can effectively prompt a robot to walk. We thus illustrate how LLMs can proficiently function as low-level feedback controllers for dynamic motion control even in high-dimensional robotic systems. The project website and source code can be found at: https://prompt2walk.github.io/ .

Shuxiao Chen, Bike Zhang, Mark W. Mueller et al.

Reinforcement learning (RL) has become a promising approach to developing controllers for quadrupedal robots. Conventionally, an RL design for locomotion follows a position-based paradigm, wherein an RL policy outputs target joint positions at a low frequency that are then tracked by a high-frequency proportional-derivative (PD) controller to produce joint torques. In contrast, for the model-based control of quadrupedal locomotion, there has been a paradigm shift from position-based control to torque-based control. In light of the recent advances in model-based control, we explore an alternative to the position-based RL paradigm, by introducing a torque-based RL framework, where an RL policy directly predicts joint torques at a high frequency, thus circumventing the use of a PD controller. The proposed learning torque control framework is validated with extensive experiments, in which a quadruped is capable of traversing various terrain and resisting external disturbances while following user-specified commands. Furthermore, compared to learning position control, learning torque control demonstrates the potential to achieve a higher reward and is more robust to significant external disturbances. To our knowledge, this is the first sim-to-real attempt for end-to-end learning torque control of quadrupedal locomotion.

Prasanth Kotaru, Guofan Wu, Koushil Sreenath

We present the coordinate-free dynamics of three different quadrotor systems : (a) single quadrotor with a point-mass payload suspended through a flexible cable; (b) multiple quadrotors with a shared point-mass payload suspended through flexible cables; and (c) multiple quadrotors with a shared rigid-body payload suspended through flexible cables. We model the flexible cable(s) as a finite series of links with spherical joints with mass concentrated at the end of each link. The resulting systems are thus high-dimensional with high degree-of-underactuation. For each of these systems, we show that the dynamics are differentially-flat, enabling planning of dynamically feasible trajectories. For the single quadrotor with a point-mass payload suspended through a flexible cable with five links (16 degrees-of-freedom and 12 degrees-of-underactuation), we use the coordinate-free dynamics to develop a geometric variation-based linearized equations of motion about a desired trajectory. We show that a finite-horizon linear quadratic regulator can be used to track a desired trajectory with a relatively large region of attraction.

Fernando Castañeda, Jason J. Choi, Wonsuhk Jung et al.

Learning-based control has recently shown great efficacy in performing complex tasks for various applications. However, to deploy it in real systems, it is of vital importance to guarantee the system will stay safe. Control Barrier Functions (CBFs) offer mathematical tools for designing safety-preserving controllers for systems with known dynamics. In this article, we first introduce a model-uncertainty-aware reformulation of CBF-based safety-critical controllers using Gaussian Process (GP) regression to close the gap between an approximate mathematical model and the real system, which results in a second-order cone program (SOCP)-based control design. We then present the pointwise feasibility conditions of the resulting safety controller, highlighting the level of richness that the available system information must meet to ensure safety. We use these conditions to devise an event-triggered online data collection strategy that ensures the recursive feasibility of the learned safety controller. Our method works by constantly reasoning about whether the current information is sufficient to ensure safety or if new measurements under active safe exploration are required to reduce the uncertainty. As a result, our proposed framework can guarantee the forward invariance of the safe set defined by the CBF with high probability, even if it contains a priori unexplored regions. We validate the proposed framework in two numerical simulation experiments.

Fernando Castañeda, Haruki Nishimura, Rowan McAllister et al.

Learning-based control approaches have shown great promise in performing complex tasks directly from high-dimensional perception data for real robotic systems. Nonetheless, the learned controllers can behave unexpectedly if the trajectories of the system divert from the training data distribution, which can compromise safety. In this work, we propose a control filter that wraps any reference policy and effectively encourages the system to stay in-distribution with respect to offline-collected safe demonstrations. Our methodology is inspired by Control Barrier Functions (CBFs), which are model-based tools from the nonlinear control literature that can be used to construct minimally invasive safe policy filters. While existing methods based on CBFs require a known low-dimensional state representation, our proposed approach is directly applicable to systems that rely solely on high-dimensional visual observations by learning in a latent state-space. We demonstrate that our method is effective for two different visuomotor control tasks in simulation environments, including both top-down and egocentric view settings.

Arjun Sripathy, Andreea Bobu, Zhongyu Li et al.

Our goal is to enable robots to perform functional tasks in emotive ways, be it in response to their users' emotional states, or expressive of their confidence levels. Prior work has proposed learning independent cost functions from user feedback for each target emotion, so that the robot may optimize it alongside task and environment specific objectives for any situation it encounters. However, this approach is inefficient when modeling multiple emotions and unable to generalize to new ones. In this work, we leverage the fact that emotions are not independent of each other: they are related through a latent space of Valence-Arousal-Dominance (VAD). Our key idea is to learn a model for how trajectories map onto VAD with user labels. Considering the distance between a trajectory's mapping and a target VAD allows this single model to represent cost functions for all emotions. As a result 1) all user feedback can contribute to learning about every emotion; 2) the robot can generate trajectories for any emotion in the space instead of only a few predefined ones; and 3) the robot can respond emotively to user-generated natural language by mapping it to a target VAD. We introduce a method that interactively learns to map trajectories to this latent space and test it in simulation and in a user study. In experiments, we use a simple vacuum robot as well as the Cassie biped.

Jason J. Choi, Donggun Lee, Boyang Li et al.

Control invariant sets are crucial for various methods that aim to design safe control policies for systems whose state constraints must be satisfied over an indefinite time horizon. In this article, we explore the connections among reachability, control invariance, and Control Barrier Functions (CBFs). Unlike prior formulations based on backward reachability concepts, we establish a strong link between these three concepts by examining the inevitable Forward Reachable Tube (FRT), which is the set of states such that every trajectory reaching the FRT must have passed through a given initial set of states. First, our findings show that the inevitable FRT is a robust control invariant set if it has a continuously differentiable boundary. If the boundary is not differentiable, the FRT may lose invariance. We also show that any robust control invariant set including the initial set is a superset of the FRT if the boundary of the invariant set is differentiable. Next, we formulate a differential game between the control and disturbance, where the inevitable FRT is characterized by the zero-superlevel set of the value function. By incorporating a discount factor in the cost function of the game, the barrier constraint of the CBF naturally arises in the Hamilton-Jacobi (HJ) equation and determines the optimal policy. The resulting FRT value function serves as a CBF-like function, and conversely, any valid CBF is also a forward reachability value function. We further prove that any $C^1$ supersolution of the HJ equation for the FRT value functions is a valid CBF and characterizes a robust control invariant set that outer-approximates the FRT. Building on this property, finally, we devise a novel method that learns neural control barrier functions, which learn an control invariant superset of the FRT of a given initial set.

Kanghyun Ryu, Qiayuan Liao, Zhongyu Li et al.

Curriculum learning is a training mechanism in reinforcement learning (RL) that facilitates the achievement of complex policies by progressively increasing the task difficulty during training. However, designing effective curricula for a specific task often requires extensive domain knowledge and human intervention, which limits its applicability across various domains. Our core idea is that large language models (LLMs), with their extensive training on diverse language data and ability to encapsulate world knowledge, present significant potential for efficiently breaking down tasks and decomposing skills across various robotics environments. Additionally, the demonstrated success of LLMs in translating natural language into executable code for RL agents strengthens their role in generating task curricula. In this work, we propose CurricuLLM, which leverages the high-level planning and programming capabilities of LLMs for curriculum design, thereby enhancing the efficient learning of complex target tasks. CurricuLLM consists of: (Step 1) Generating sequence of subtasks that aid target task learning in natural language form, (Step 2) Translating natural language description of subtasks in executable task code, including the reward code and goal distribution code, and (Step 3) Evaluating trained policies based on trajectory rollout and subtask description. We evaluate CurricuLLM in various robotics simulation environments, ranging from manipulation, navigation, and locomotion, to show that CurricuLLM can aid learning complex robot control tasks. In addition, we validate humanoid locomotion policy learned through CurricuLLM in real-world. Project website is https://iconlab.negarmehr.com/CurricuLLM/

Zhen Wu, Xiaoyu Huang, Lujie Yang et al.

While recent advances in humanoid locomotion have achieved stable walking on varied terrains, capturing the agility and adaptivity of highly dynamic human motions remains an open challenge. In particular, agile parkour in complex environments demands not only low-level robustness, but also human-like motion expressiveness, long-horizon skill composition, and perception-driven decision-making. In this paper, we present Perceptive Humanoid Parkour (PHP), a modular framework that enables humanoid robots to autonomously perform long-horizon, vision-based parkour across challenging obstacle courses. Our approach first leverages motion matching, formulated as nearest-neighbor search in a feature space, to compose retargeted atomic human skills into long-horizon kinematic trajectories. This framework enables the flexible composition and smooth transition of complex skill chains while preserving the elegance and fluidity of dynamic human motions. Next, we train motion-tracking reinforcement learning (RL) expert policies for these composed motions, and distill them into a single depth-based, multi-skill student policy, using a combination of DAgger and RL. Crucially, the combination of perception and skill composition enables autonomous, context-aware decision-making: using only onboard depth sensing and a discrete 2D velocity command, the robot selects and executes whether to step over, climb onto, vault or roll off obstacles of varying geometries and heights. We validate our framework with extensive real-world experiments on a Unitree G1 humanoid robot, demonstrating highly dynamic parkour skills such as climbing tall obstacles up to 1.25m (96% robot height), as well as long-horizon multi-obstacle traversal with closed-loop adaptation to real-time obstacle perturbations.

Haozhi Qi, Yen-Jen Wang, Toru Lin et al.

Humanoid robots hold great promise for operating in human-centric environments, yet achieving robust whole-body coordination across the head, hands, and legs remains a major challenge. We present a system that combines a modular teleoperation interface with a scalable learning framework to address this problem. Our teleoperation design decomposes humanoid control into intuitive submodules, which include hand-eye coordination, grasp primitives, arm end-effector tracking, and locomotion. This modularity allows us to collect high-quality demonstrations efficiently. Building on this, we introduce Choice Policy, an imitation learning approach that generates multiple candidate actions and learns to score them. This architecture enables both fast inference and effective modeling of multimodal behaviors. We validate our approach on two real-world tasks: dishwasher loading and whole-body loco-manipulation for whiteboard wiping. Experiments show that Choice Policy significantly outperforms diffusion policies and standard behavior cloning. Furthermore, our results indicate that hand-eye coordination is critical for success in long-horizon tasks. Our work demonstrates a practical path toward scalable data collection and learning for coordinated humanoid manipulation in unstructured environments.

Mintae Kim, Koushil Sreenath

Reinforcement learning (RL) policies often fail under dynamics that differ from training, a gap not fully addressed by domain randomization or existing adversarial RL methods. Distributionally robust RL provides a formal remedy but still relies on surrogate adversaries to approximate intractable primal problems, leaving blind spots that potentially cause instability and over-conservatism. We propose a dual formulation that directly exposes the robustness-performance trade-off. At the trajectory level, a temperature parameter from the dual problem is approximated with an adversarial network, yielding efficient and stable worst-case rollouts within a divergence bound. At the model level, we employ Boltzmann reweighting over dynamics ensembles, focusing on more adverse environments to the current policy rather than uniform sampling. The two components act independently and complement each other: trajectory-level steering ensures robust rollouts, while model-level sampling provides policy-sensitive coverage of adverse dynamics. The resulting framework, robust adversarial policy optimization (RAPO) outperforms robust RL baselines, improving resilience to uncertainty and generalization to out-of-distribution dynamics while maintaining dual tractability.

Mintae Kim, Koushil Sreenath

Reinforcement learning (RL) in robotics is often limited by the cost and risk of data collection, motivating experience transfer from a source task to a target task. Offline-to-online RL leverages prior data but typically assumes a given fixed dataset and does not address how to generate reliable data for transfer. We propose \textit{World Model-based Experience Transfer} (WOMBET), a framework that jointly generates and utilizes prior data. WOMBET learns a world model in the source task and generates offline data via uncertainty-penalized planning, followed by filtering trajectories with high return and low epistemic uncertainty. It then performs online fine-tuning in the target task using adaptive sampling between offline and online data, enabling a stable transition from prior-driven initialization to task-specific adaptation. We show that the uncertainty-penalized objective provides a lower bound on the true return and derive a finite-sample error decomposition capturing distribution mismatch and approximation error. Empirically, WOMBET improves sample efficiency and final performance over strong baselines on continuous control benchmarks, demonstrating the benefit of jointly optimizing data generation and transfer.

Xingpeng Xia, Jason J. Choi, Ayush Agrawal et al.

Learning-based approaches have recently shown notable success in legged locomotion. However, these approaches often lack accountability, necessitating empirical tests to determine their effectiveness. In this work, we are interested in designing a learning-based locomotion controller whose stability can be examined and guaranteed. This can be achieved by verifying regions of attraction (RoAs) of legged robots to their stable walking gaits. This is a non-trivial problem for legged robots due to their hybrid dynamics. Although previous work has shown the utility of Hamilton-Jacobi (HJ) reachability to solve this problem, its practicality was limited by its poor scalability. The core contribution of our work is the employment of a deep learning-based HJ reachability solution to the hybrid legged robot dynamics, which overcomes the previous work's limitation. With the learned reachability solution, first, we can estimate a library of RoAs for various gaits. Second, we can design a one-step predictive controller that effectively stabilizes to an individual gait within the verified RoA. Finally, we can devise a strategy that switches gaits, in response to external perturbations, whose feasibility is guided by the RoA analysis. We demonstrate our method in a two-link walker simulation, whose mathematical model is well established. Our method achieves improved stability than previous model-based methods, while ensuring transparency that was not present in the existing learning-based approaches.

Hanwen Wang, Qiayuan Liao, Bike Zhang et al.

Human motion provides rich priors for training general-purpose humanoid control policies, but raw demonstrations are often incompatible with a robot's kinematics and dynamics, limiting their direct use. We present a two-stage pipeline for generating natural and dynamically feasible motion references from task-space human data. First, we convert human motion into a unified robot description format (URDF)-based skeleton representation and calibrate it to the target humanoid's dimensions. By aligning the underlying skeleton structure rather than heuristically modifying task-space targets, this step significantly reduces inverse kinematics error and tuning effort. Second, we refine the retargeted trajectories through progressive kinodynamic trajectory optimization (TO), solved in three stages: kinematic TO, inverse dynamics, and full kinodynamic TO, each warm-started from the previous solution. The final result yields dynamically consistent state trajectories and joint torque profiles, providing high-quality references for learning-based controllers. Together, skeleton calibration and kinodynamic TO enable the generation of natural, physically consistent motion references across diverse humanoid platforms.

Sangli Teng, Hang Liu, Jingyu Song et al.

Learning the flows of hybrid systems that have both continuous and discrete time dynamics is challenging. The existing method learns the dynamics in each discrete mode, which suffers from the combination of mode switching and discontinuities in the flows. In this work, we propose CHyLL (Continuous Hybrid System Learning in Latent Space), which learns a continuous neural representation of a hybrid system without trajectory segmentation, event functions, or mode switching. The key insight of CHyLL is that the reset map glues the state space at the guard surface, reformulating the state space as a piecewise smooth quotient manifold where the flow becomes spatially continuous. Building upon these insights and the embedding theorems grounded in differential topology, CHyLL concurrently learns a singularity-free neural embedding in a higher-dimensional space and the continuous flow in it. We showcase that CHyLL can accurately predict the flow of hybrid systems with superior accuracy and identify the topological invariants of the hybrid systems. Finally, we apply CHyLL to the stochastic optimal control problem.

Zhongyu Li, Xue Bin Peng, Pieter Abbeel et al.

This paper presents a comprehensive study on using deep reinforcement learning (RL) to create dynamic locomotion controllers for bipedal robots. Going beyond focusing on a single locomotion skill, we develop a general control solution that can be used for a range of dynamic bipedal skills, from periodic walking and running to aperiodic jumping and standing. Our RL-based controller incorporates a novel dual-history architecture, utilizing both a long-term and short-term input/output (I/O) history of the robot. This control architecture, when trained through the proposed end-to-end RL approach, consistently outperforms other methods across a diverse range of skills in both simulation and the real world. The study also delves into the adaptivity and robustness introduced by the proposed RL system in developing locomotion controllers. We demonstrate that the proposed architecture can adapt to both time-invariant dynamics shifts and time-variant changes, such as contact events, by effectively using the robot's I/O history. Additionally, we identify task randomization as another key source of robustness, fostering better task generalization and compliance to disturbances. The resulting control policies can be successfully deployed on Cassie, a torque-controlled human-sized bipedal robot. This work pushes the limits of agility for bipedal robots through extensive real-world experiments. We demonstrate a diverse range of locomotion skills, including: robust standing, versatile walking, fast running with a demonstration of a 400-meter dash, and a diverse set of jumping skills, such as standing long jumps and high jumps.

Mintae Kim, Jiaze Cai, Koushil Sreenath

Designing robust controllers for precise trajectory tracking with quadrotors is challenging due to nonlinear dynamics and underactuation, and becomes harder with flexible cable-suspended payloads that add degrees of freedom and hybrid dynamics. Classical model-based methods offer stability guarantees but require extensive tuning and often fail to adapt when the configuration changes-when a payload is added or removed, or when its mass or cable length varies. We present RoVerFly, a unified learning-based control framework where a single reinforcement learning (RL) policy functions as an implicit hybrid controller, managing complex dynamics without explicit mode detection or controller switching. Trained with task and domain randomization, the controller is resilient to disturbances and varying dynamics. It achieves strong zero-shot generalization across payload settings-including no payload as well as varying mass and cable length-without re-tuning, while retaining the interpretability and structure of a feedback tracking controller. Code and supplementary materials are available at https://github.com/mintaeshkim/roverfly.

Ilija Radosavovic, Bike Zhang, Baifeng Shi et al.

We cast real-world humanoid control as a next token prediction problem, akin to predicting the next word in language. Our model is a causal transformer trained via autoregressive prediction of sensorimotor trajectories. To account for the multi-modal nature of the data, we perform prediction in a modality-aligned way, and for each input token predict the next token from the same modality. This general formulation enables us to leverage data with missing modalities, like video trajectories without actions. We train our model on a collection of simulated trajectories coming from prior neural network policies, model-based controllers, motion capture data, and YouTube videos of humans. We show that our model enables a full-sized humanoid to walk in San Francisco zero-shot. Our model can transfer to the real world even when trained on only 27 hours of walking data, and can generalize to commands not seen during training like walking backward. These findings suggest a promising path toward learning challenging real-world control tasks by generative modeling of sensorimotor trajectories.

Yucheng Hu, Yanjiang Guo, Pengchao Wang et al.

Visual representations play a crucial role in developing generalist robotic policies. Previous vision encoders, typically pre-trained with single-image reconstruction or two-image contrastive learning, tend to capture static information, often neglecting the dynamic aspects vital for embodied tasks. Recently, video diffusion models (VDMs) demonstrate the ability to predict future frames and showcase a strong understanding of physical world. We hypothesize that VDMs inherently produce visual representations that encompass both current static information and predicted future dynamics, thereby providing valuable guidance for robot action learning. Based on this hypothesis, we propose the Video Prediction Policy (VPP), which learns implicit inverse dynamics model conditioned on predicted future representations inside VDMs. To predict more precise future, we fine-tune pre-trained video foundation model on robot datasets along with internet human manipulation data. In experiments, VPP achieves a 18.6\% relative improvement on the Calvin ABC-D generalization benchmark compared to the previous state-of-the-art, and demonstrates a 31.6\% increase in success rates for complex real-world dexterous manipulation tasks. Project page at https://video-prediction-policy.github.io

Zixuan Chen, Xialin He, Yen-Jen Wang et al.

Reinforcement learning combined with sim-to-real transfer offers a general framework for developing locomotion controllers for legged robots. To facilitate successful deployment in the real world, smoothing techniques, such as low-pass filters and smoothness rewards, are often employed to develop policies with smooth behaviors. However, because these techniques are non-differentiable and usually require tedious tuning of a large set of hyperparameters, they tend to require extensive manual tuning for each robotic platform. To address this challenge and establish a general technique for enforcing smooth behaviors, we propose a simple and effective method that imposes a Lipschitz constraint on a learned policy, which we refer to as Lipschitz-Constrained Policies (LCP). We show that the Lipschitz constraint can be implemented in the form of a gradient penalty, which provides a differentiable objective that can be easily incorporated with automatic differentiation frameworks. We demonstrate that LCP effectively replaces the need for smoothing rewards or low-pass filters and can be easily integrated into training frameworks for many distinct humanoid robots. We extensively evaluate LCP in both simulation and real-world humanoid robots, producing smooth and robust locomotion controllers. All simulation and deployment code, along with complete checkpoints, is available on our project page: https://lipschitz-constrained-policy.github.io.

Zhengmao He, Kun Lei, Yanjie Ze et al.

Quadruped robots are progressively being integrated into human environments. Despite the growing locomotion capabilities of quadrupedal robots, their interaction with objects in realistic scenes is still limited. While additional robotic arms on quadrupedal robots enable manipulating objects, they are sometimes redundant given that a quadruped robot is essentially a mobile unit equipped with four limbs, each possessing 3 degrees of freedom (DoFs). Hence, we aim to empower a quadruped robot to execute real-world manipulation tasks using only its legs. We decompose the loco-manipulation process into a low-level reinforcement learning (RL)-based controller and a high-level Behavior Cloning (BC)-based planner. By parameterizing the manipulation trajectory, we synchronize the efforts of the upper and lower layers, thereby leveraging the advantages of both RL and BC. Our approach is validated through simulations and real-world experiments, demonstrating the robot's ability to perform tasks that demand mobility and high precision, such as lifting a basket from the ground while moving, closing a dishwasher, pressing a button, and pushing a door. Project website: https://zhengmaohe.github.io/leg-manip

Will Lavanakul, Jason J. Choi, Koushil Sreenath et al.

Learning-based approaches are emerging as an effective approach for safety filters for black-box dynamical systems. Existing methods have relied on certificate functions like Control Barrier Functions (CBFs) and Hamilton-Jacobi (HJ) reachability value functions. The primary motivation for our work is the recognition that ultimately, enforcing the safety constraint as a control input constraint at each state is what matters. By focusing on this constraint, we can eliminate dependence on any specific certificate function-based design. To achieve this, we define a discriminating hyperplane that shapes the half-space constraint on control input at each state, serving as a sufficient condition for safety. This concept not only generalizes over traditional safety methods but also simplifies safety filter design by eliminating dependence on specific certificate functions. We present two strategies to learn the discriminating hyperplane: (a) a supervised learning approach, using pre-verified control invariant sets for labeling, and (b) a reinforcement learning (RL) approach, which does not require such labels. The main advantage of our method, unlike conventional safe RL approaches, is the separation of performance and safety. This offers a reusable safety filter for learning new tasks, avoiding the need to retrain from scratch. As such, we believe that the new notion of the discriminating hyperplane offers a more generalizable direction towards designing safety filters, encompassing and extending existing certificate-function-based or safe RL methodologies.

Tong Zhang, Boyuan Zheng, Ruiqian Nai et al.

The human body demonstrates exceptional motor capabilities-such as standing steadily on one foot or performing a high kick with the leg raised over 1.5 meters-both requiring precise balance control. While recent research on humanoid control has leveraged reinforcement learning to track human motions for skill acquisition, applying this paradigm to balance-intensive tasks remains challenging. In this work, we identify three key obstacles: instability from reference motion errors, learning difficulties due to morphological mismatch, and the sim-to-real gap caused by sensor noise and unmodeled dynamics. To address these challenges, we propose HuB (Humanoid Balance), a unified framework that integrates reference motion refinement, balance-aware policy learning, and sim-to-real robustness training, with each component targeting a specific challenge. We validate our approach on the Unitree G1 humanoid robot across challenging quasi-static balance tasks, including extreme single-legged poses such as Swallow Balance and Bruce Lee's Kick. Our policy remains stable even under strong physical disturbances-such as a forceful soccer strike-while baseline methods consistently fail to complete these tasks. Project website: https://hub-robot.github.io

Haoru Xue, Xiaoyu Huang, Dantong Niu et al.

Vision-language-action (VLA) models have demonstrated strong semantic understanding and zero-shot generalization, yet most existing systems assume an accurate low-level controller with hand-crafted action "vocabulary" such as end-effector pose or root velocity. This assumption confines prior work to quasi-static tasks and precludes the agile, whole-body behaviors required by humanoid whole-body control (WBC) tasks. To capture this gap in the literature, we start by introducing the first sim-to-real-ready, vision-language, closed-loop benchmark for humanoid WBC, comprising over 150 tasks from 10 categories. We then propose LeVERB: Latent Vision-Language-Encoded Robot Behavior, a hierarchical latent instruction-following framework for humanoid vision-language WBC, the first of its kind. At the top level, a vision-language policy learns a latent action vocabulary from synthetically rendered kinematic demonstrations; at the low level, a reinforcement-learned WBC policy consumes these latent verbs to generate dynamics-level commands. In our benchmark, LeVERB can zero-shot attain a 80% success rate on simple visual navigation tasks, and 58.5% success rate overall, outperforming naive hierarchical whole-body VLA implementation by 7.8 times.

Xiaoyu Huang, Takara Truong, Yunbo Zhang et al.

We present Diffuse-CLoC, a guided diffusion framework for physics-based look-ahead control that enables intuitive, steerable, and physically realistic motion generation. While existing kinematics motion generation with diffusion models offer intuitive steering capabilities with inference-time conditioning, they often fail to produce physically viable motions. In contrast, recent diffusion-based control policies have shown promise in generating physically realizable motion sequences, but the lack of kinematics prediction limits their steerability. Diffuse-CLoC addresses these challenges through a key insight: modeling the joint distribution of states and actions within a single diffusion model makes action generation steerable by conditioning it on the predicted states. This approach allows us to leverage established conditioning techniques from kinematic motion generation while producing physically realistic motions. As a result, we achieve planning capabilities without the need for a high-level planner. Our method handles a diverse set of unseen long-horizon downstream tasks through a single pre-trained model, including static and dynamic obstacle avoidance, motion in-betweening, and task-space control. Experimental results show that our method significantly outperforms the traditional hierarchical framework of high-level motion diffusion and low-level tracking.

Zhi Su, Yuman Gao, Emily Lukas et al. · bytedance

Achieving coordinated teamwork among legged robots requires both fine-grained locomotion control and long-horizon strategic decision-making. Robot soccer offers a compelling testbed for this challenge, combining dynamic, competitive, and multi-agent interactions. In this work, we present a hierarchical multi-agent reinforcement learning (MARL) framework that enables fully autonomous and decentralized quadruped robot soccer. First, a set of highly dynamic low-level skills is trained for legged locomotion and ball manipulation, such as walking, dribbling, and kicking. On top of these, a high-level strategic planning policy is trained with Multi-Agent Proximal Policy Optimization (MAPPO) via Fictitious Self-Play (FSP). This learning framework allows agents to adapt to diverse opponent strategies and gives rise to sophisticated team behaviors, including coordinated passing, interception, and dynamic role allocation. With an extensive ablation study, the proposed learning method shows significant advantages in the cooperative and competitive multi-agent soccer game. We deploy the learned policies to real quadruped robots relying solely on onboard proprioception and decentralized localization, with the resulting system supporting autonomous robot-robot and robot-human soccer matches on indoor and outdoor soccer courts.

Hang Liu, Yuman Gao, Sangli Teng et al.

Enabling humanoid robots to exploit physical contact, rather than simply avoid collisions, is crucial for autonomy in unstructured environments. Traditional optimization-based planners struggle with contact complexity, while on-policy reinforcement learning (RL) is sample-inefficient and has limited multi-task ability. We propose a framework combining a learned world model with sampling-based Model Predictive Control (MPC), trained on a demonstration-free offline dataset to predict future outcomes in a compressed latent space. To address sparse contact rewards and sensor noise, the MPC uses a learned surrogate value function for dense, robust planning. Our single, scalable model supports contact-aware tasks, including wall support after perturbation, blocking incoming objects, and traversing height-limited arches, with improved data efficiency and multi-task capability over on-policy RL. Deployed on a physical humanoid, our system achieves robust, real-time contact planning from proprioception and ego-centric depth images. Website: https://ego-vcp.github.io/

Jason J. Choi, Ayush Agrawal, Koushil Sreenath et al.

Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the discontinuous state changes upon contact (also referred to as state resets). In this work, we cast the computation of region-ofattraction as a Hamilton-Jacobi (HJ) reachability problem. This enables us to leverage HJ reachability tools that are compatible with general nonlinear system dynamics, and can formally deal with state and input constraints as well as bounded disturbances. Our main contribution is the generalization of HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions for several underactuated walking robots and demonstrate that the proposed approach can (a) recover a bigger region-of-attraction than state-of-the-art approaches, (b) handle state resets, nonlinear dynamics, external disturbances, and input constraints, and (c) also provides a stabilizing controller for the system that can leverage the state resets for enhancing system stability.

Hengbo Ma, Bike Zhang, Masayoshi Tomizuka et al.

Control barrier functions (CBFs) have become a popular tool to enforce safety of a control system. CBFs are commonly utilized in a quadratic program formulation (CBF-QP) as safety-critical constraints. A class $\mathcal{K}$ function in CBFs usually needs to be tuned manually in order to balance the trade-off between performance and safety for each environment. However, this process is often heuristic and can become intractable for high relative-degree systems. Moreover, it prevents the CBF-QP from generalizing to different environments in the real world. By embedding the optimization procedure of the exponential control barrier function based quadratic program (ECBF-QP) as a differentiable layer within a deep learning architecture, we propose a differentiable safety-critical control framework that enables generalization to new environments for high relative-degree systems with forward invariance guarantees. Finally, we validate the proposed control design with 2D double and quadruple integrator systems in various environments.

Suiyi He, Jun Zeng, Koushil Sreenath

This paper presents a novel planning and control strategy for competing with multiple vehicles in a car racing scenario. The proposed racing strategy switches between two modes. When there are no surrounding vehicles, a learning-based model predictive control (MPC) trajectory planner is used to guarantee that the ego vehicle achieves better lap timing performance. When the ego vehicle is competing with other surrounding vehicles to overtake, an optimization-based planner generates multiple dynamically-feasible trajectories through parallel computation. Each trajectory is optimized under a MPC formulation with different homotopic Bezier-curve reference paths lying laterally between surrounding vehicles. The time-optimal trajectory among these different homotopic trajectories is selected and a low-level MPC controller with control barrier function constraints for obstacle avoidance is used to guarantee system's safety-critical performance. The proposed algorithm has the capability to generate collision-free trajectories and track them while enhancing the lap timing performance with steady low computational complexity, outperforming existing approaches in both timing and performance for a autonomous racing environment. To demonstrate the performance of our racing strategy, we simulate with multiple randomly generated moving vehicles on the track and test the ego vehicle's overtake maneuvers.

Ayush Agrawal, Shuxiao Chen, Akshara Rai et al.

In this paper, we present a framework rooted in control and planning that enables quadrupedal robots to traverse challenging terrains with discrete footholds using visual feedback. Navigating discrete terrain is challenging for quadrupeds because the motion of the robot can be aperiodic, highly dynamic, and blind for the hind legs of the robot. Additionally, the robot needs to reason over both the feasible footholds as well as robot velocity by speeding up and slowing down at different parts of the terrain. We build an offline library of periodic gaits which span two trotting steps on the robot, and switch between different motion primitives to achieve aperiodic motions of different step lengths on an A1 robot. The motion library is used to provide targets to a geometric model predictive controller which controls stance. To incorporate visual feedback, we use terrain mapping tools to build a local height map of the terrain around the robot using RGB and depth cameras, and extract feasible foothold locations around both the front and hind legs of the robot. Our experiments show a Unitree A1 robot navigating multiple unknown, challenging and discrete terrains in the real world.

Akshay Thirugnanam, Jun Zeng, Koushil Sreenath

Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.

Zhongyu Li, Jun Zeng, Shuxiao Chen et al.

Navigating a large-scaled robot in unknown and cluttered height-constrained environments is challenging. Not only is a fast and reliable planning algorithm required to go around obstacles, the robot should also be able to change its intrinsic dimension by crouching in order to travel underneath height-constrained regions. There are few mobile robots that are capable of handling such a challenge, and bipedal robots provide a solution. However, as bipedal robots have nonlinear and hybrid dynamics, trajectory planning while ensuring dynamic feasibility and safety on these robots is challenging. This paper presents an end-to-end autonomous navigation framework which leverages three layers of planners and a variable walking height controller to enable bipedal robots to safely explore height-constrained environments. A vertically-actuated Spring-Loaded Inverted Pendulum (vSLIP) model is introduced to capture the robot's coupled dynamics of planar walking and vertical walking height. This reduced-order model is utilized to optimize for long-term and short-term safe trajectory plans. A variable walking height controller is leveraged to enable the bipedal robot to maintain stable periodic walking gaits while following the planned trajectory. The entire framework is tested and experimentally validated using a bipedal robot Cassie. This demonstrates reliable autonomy to drive the robot to safely avoid obstacles while walking to the goal location in various kinds of height-constrained cluttered environments.

Shuxiao Chen, Xiangyu Wu, Mark W. Mueller et al.

The capabilities of autonomous flight with unmanned aerial vehicles (UAVs) have significantly increased in recent times. However, basic problems such as fast and robust geo-localization in GPS-denied environments still remain unsolved. Existing research has primarily concentrated on improving the accuracy of localization at the cost of long and varying computation time in various situations, which often necessitates the use of powerful ground station machines. In order to make image-based geo-localization online and pragmatic for lightweight embedded systems on UAVs, we propose a framework that is reliable in changing scenes, flexible about computing resource allocation and adaptable to common camera placements. The framework is comprised of two stages: offline database preparation and online inference. At the first stage, color images and depth maps are rendered as seen from potential vehicle poses quantized over the satellite and topography maps of anticipated flying areas. A database is then populated with the global and local descriptors of the rendered images. At the second stage, for each captured real-world query image, top global matches are retrieved from the database and the vehicle pose is further refined via local descriptor matching. We present field experiments of image-based localization on two different UAV platforms to validate our results.

Akshay Thirugnanam, Jun Zeng, Koushil Sreenath

Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in tight spaces. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization problem. To address these challenges, we propose a duality-based safety-critical optimal control using nonsmooth control barrier functions for obstacle avoidance between polytopes, which can be solved in real-time with a QP-based optimization problem. A dual optimization problem is introduced to represent the minimum distance between polytopes and the Lagrangian function for the dual form is applied to construct a control barrier function. We validate the obstacle avoidance with the proposed dual formulation for L-shaped (sofa-shaped) controlled robot in a corridor environment. We demonstrate real-time tight obstacle avoidance with non-conservative maneuvers on a moving sofa (piano) problem with nonlinear dynamics.

Scott Gilroy, Derek Lau, Lizhi Yang et al.

Quadrupeds are strong candidates for navigating challenging environments because of their agile and dynamic designs. This paper presents a methodology that extends the range of exploration for quadrupedal robots by creating an end-to-end navigation framework that exploits walking and jumping modes. To obtain a dynamic jumping maneuver while avoiding obstacles, dynamically-feasible trajectories are optimized offline through collocation-based optimization where safety constraints are imposed. Such optimization schematic allows the robot to jump through window-shaped obstacles by considering both obstacles in the air and on the ground. The resulted jumping mode is utilized in an autonomous navigation pipeline that leverages a search-based global planner and a local planner to enable the robot to reach the goal location by walking. A state machine together with a decision making strategy allows the system to switch behaviors between walking around obstacles or jumping through them. The proposed framework is experimentally deployed and validated on a quadrupedal robot, a Mini Cheetah, to enable the robot to autonomously navigate through an environment while avoiding obstacles and jumping over a maximum height of 13 cm to pass through a window-shaped opening in order to reach its goal.

Fernando Castañeda, Jason J. Choi, Bike Zhang et al.

Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a min-norm quadratic program (CBF-CLF-QP) which solves for a safety-critical control input. However, since these constraints rely on a model of the system, when this model is inaccurate the guarantees of safety and stability can be easily lost. In this paper, we present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs. The considered model uncertainty is affected by both state and control input. We derive probabilistic bounds on the effects that such model uncertainty has on the dynamics of the CBF and CLF. We then use these bounds to build safety and stability chance constraints that can be incorporated in a min-norm convex optimization-based controller, called GP-CBF-CLF-SOCP. As the main theoretical result of the paper, we present necessary and sufficient conditions for pointwise feasibility of the proposed optimization problem. We believe that these conditions could serve as a starting point towards understanding what are the minimal requirements on the distribution of data collected from the real system in order to guarantee safety. Finally, we validate the proposed framework with numerical simulations of an adaptive cruise controller for an automotive system.