Fábio Ramos

Jie Xu, Viktor Makoviychuk, Yashraj Narang et al. · gatech, nvidia

Deep reinforcement learning can generate complex control policies, but requires large amounts of training data to work effectively. Recent work has attempted to address this issue by leveraging differentiable simulators. However, inherent problems such as local minima and exploding/vanishing numerical gradients prevent these methods from being generally applied to control tasks with complex contact-rich dynamics, such as humanoid locomotion in classical RL benchmarks. In this work we present a high-performance differentiable simulator and a new policy learning algorithm (SHAC) that can effectively leverage simulation gradients, even in the presence of non-smoothness. Our learning algorithm alleviates problems with local minima through a smooth critic function, avoids vanishing/exploding gradients through a truncated learning window, and allows many physical environments to be run in parallel. We evaluate our method on classical RL control tasks, and show substantial improvements in sample efficiency and wall-clock time over state-of-the-art RL and differentiable simulation-based algorithms. In addition, we demonstrate the scalability of our method by applying it to the challenging high-dimensional problem of muscle-actuated locomotion with a large action space, achieving a greater than 17x reduction in training time over the best-performing established RL algorithm.

Eric Heiden, Miles Macklin, Yashraj Narang et al. · gatech, nvidia

Robotic cutting of soft materials is critical for applications such as food processing, household automation, and surgical manipulation. As in other areas of robotics, simulators can facilitate controller verification, policy learning, and dataset generation. Moreover, differentiable simulators can enable gradient-based optimization, which is invaluable for calibrating simulation parameters and optimizing controllers. In this work, we present DiSECt: the first differentiable simulator for cutting soft materials. The simulator augments the finite element method (FEM) with a continuous contact model based on signed distance fields (SDF), as well as a continuous damage model that inserts springs on opposite sides of the cutting plane and allows them to weaken until zero stiffness, enabling crack formation. Through various experiments, we evaluate the performance of the simulator. We first show that the simulator can be calibrated to match resultant forces and deformation fields from a state-of-the-art commercial solver and real-world cutting datasets, with generality across cutting velocities and object instances. We then show that Bayesian inference can be performed efficiently by leveraging the differentiability of the simulator, estimating posteriors over hundreds of parameters in a fraction of the time of derivative-free methods. Next, we illustrate that control parameters in the simulation can be optimized to minimize cutting forces via lateral slicing motions. Finally, we conduct experiments on a real robot arm equipped with a slicing knife to infer simulation parameters from force measurements. By optimizing the slicing motion of the knife, we show on fruit cutting scenarios that the average knife force can be reduced by more than 40% compared to a vertical cutting motion. We publish code and additional materials on our project website at https://diff-cutting-sim.github.io.

Yewon Lee, Andrew Z. Li, Philip Huang et al. · mit

Planning for sequential robotics tasks often requires integrated symbolic and geometric reasoning. TAMP algorithms typically solve these problems by performing a tree search over high-level task sequences while checking for kinematic and dynamic feasibility. This can be inefficient because, typically, candidate task plans resulting from the tree search ignore geometric information. This often leads to motion planning failures that require expensive backtracking steps to find alternative task plans. We propose a novel approach to TAMP called Stein Task and Motion Planning (STAMP) that relaxes the hybrid optimization problem into a continuous domain. This allows us to leverage gradients from differentiable physics simulation to fully optimize discrete and continuous plan parameters for TAMP. In particular, we solve the optimization problem using a gradient-based variational inference algorithm called Stein Variational Gradient Descent. This allows us to find a distribution of solutions within a single optimization run. Furthermore, we use an off-the-shelf differentiable physics simulator that is parallelized on the GPU to run parallelized inference over diverse plan parameters. We demonstrate our method on a variety of problems and show that it can find multiple diverse plans in a single optimization run while also being significantly faster than existing approaches.

Tin Lai, Weiming Zhi, Tucker Hermans et al. · nvidia

We present the Learning for KinoDynamic Tree Expansion (L4KDE) method for kinodynamic planning. Tree-based planning approaches, such as rapidly exploring random tree (RRT), are the dominant approach to finding globally optimal plans in continuous state-space motion planning. Central to these approaches is tree-expansion, the procedure in which new nodes are added into an ever-expanding tree. We study the kinodynamic variants of tree-based planning, where we have known system dynamics and kinematic constraints. In the interest of quickly selecting nodes to connect newly sampled coordinates, existing methods typically cannot optimise to find nodes that have low cost to transition to sampled coordinates. Instead, they use metrics like Euclidean distance between coordinates as a heuristic for selecting candidate nodes to connect to the search tree. We propose L4KDE to address this issue. L4KDE uses a neural network to predict transition costs between queried states, which can be efficiently computed in batch, providing much higher quality estimates of transition cost compared to commonly used heuristics while maintaining almost-surely asymptotic optimality guarantee. We empirically demonstrate the significant performance improvement provided by L4KDE on a variety of challenging system dynamics, with the ability to generalise across different instances of the same model class, and in conjunction with a suite of modern tree-based motion planners.

Lucas Barcelos, Tin Lai, Rafael Oliveira et al.

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. Our approach builds on path signatures and Hilbert space representations of trajectories, and connects parallel variational inference for trajectory estimation with diversity promoting kernels. We empirically demonstrate that this strategy achieves lower average costs than competing alternatives on a range of problems, from 2D navigation to robotic manipulators operating in cluttered environments.

Jayadeep Jacob, Tirthankar Bandyopadhyay, Jason Williams et al.

We propose to use a simulation driven inverse inference approach to model the dynamics of tree branches under manipulation. Learning branch dynamics and gaining the ability to manipulate deformable vegetation can help with occlusion-prone tasks, such as fruit picking in dense foliage, as well as moving overhanging vines and branches for navigation in dense vegetation. The underlying deformable tree geometry is encapsulated as coarse spring abstractions executed on parallel, non-differentiable simulators. The implicit statistical model defined by the simulator, reference trajectories obtained by actively probing the ground truth, and the Bayesian formalism, together guide the spring parameter posterior density estimation. Our non-parametric inference algorithm, based on Stein Variational Gradient Descent, incorporates biologically motivated assumptions into the inference process as neural network driven learnt joint priors; moreover, it leverages the finite difference scheme for gradient approximations. Real and simulated experiments confirm that our model can predict deformation trajectories, quantify the estimation uncertainty, and it can perform better when base-lined against other inference algorithms, particularly from the Monte Carlo family. The model displays strong robustness properties in the presence of heteroscedastic sensor noise; furthermore, it can generalise to unseen grasp locations.

Rafael Oliveira, Louis Tiao, Fabio Ramos

Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.

Rel Guzman, Rafael Oliveira, Fabio Ramos

We propose an adaptive optimisation approach for tuning stochastic model predictive control (MPC) hyper-parameters while jointly estimating probability distributions of the transition model parameters based on performance rewards. In particular, we develop a Bayesian optimisation (BO) algorithm with a heteroscedastic noise model to deal with varying noise across the MPC hyper-parameter and dynamics model parameter spaces. Typical homoscedastic noise models are unrealistic for tuning MPC since stochastic controllers are inherently noisy, and the level of noise is affected by their hyper-parameter settings. We evaluate the proposed optimisation algorithm in simulated control and robotics tasks where we jointly infer control and dynamics parameters. Experimental results demonstrate that our approach leads to higher cumulative rewards and more stable controllers.

Julia Tan, Ransalu Senanayake, Fabio Ramos

Deep reinforcement learning (RL) is a promising approach to solving complex robotics problems. However, the process of learning through trial-and-error interactions is often highly time-consuming, despite recent advancements in RL algorithms. Additionally, the success of RL is critically dependent on how well the reward-shaping function suits the task, which is also time-consuming to design. As agents trained on a variety of robotics problems continue to proliferate, the ability to reuse their valuable learning for new domains becomes increasingly significant. In this paper, we propose a post-hoc technique for policy fusion using Optimal Transport theory as a robust means of consolidating the knowledge of multiple agents that have been trained on distinct scenarios. We further demonstrate that this provides an improved weights initialisation of the neural network policy for learning new tasks, requiring less time and computational resources than either retraining the parent policies or training a new policy from scratch. Ultimately, our results on diverse agents commonly used in deep RL show that specialised knowledge can be unified into a "Renaissance agent", allowing for quicker learning of new skills.

Rel Guzman, Rafael Oliveira, Fabio Ramos

Stochastic model predictive control has been a successful and robust control framework for many robotics tasks where the system dynamics model is slightly inaccurate or in the presence of environment disturbances. Despite the successes, it is still unclear how to best adjust control parameters to the current task in the presence of model parameter uncertainty and heteroscedastic noise. In this paper, we propose an adaptive MPC variant that automatically estimates control and model parameters by leveraging ideas from Bayesian optimisation (BO) and the classical expected improvement acquisition function. We leverage recent results showing that BO can be reformulated via density ratio estimation, which can be efficiently approximated by simply learning a classifier. This is then integrated into a model predictive path integral control framework yielding robust controllers for a variety of challenging robotics tasks. We demonstrate the approach on classical control problems under model uncertainty and robotics manipulation tasks.

Caelan Garrett, Fabio Ramos

Bimanual and humanoid robots are appealing because of their human-like ability to leverage multiple arms to efficiently complete tasks. However, controlling multiple arms at once is computationally challenging due to the growth in the hybrid discrete-continuous action space. Task and Motion Planning (TAMP) algorithms can efficiently plan in hybrid spaces but generally produce plans, where only one arm is moving at a time, rather than schedules that allow for parallel arm motion. In order to extend TAMP to produce schedules, we present ScheduleStream, the first general-purpose framework for planning & scheduling with sampling operations. ScheduleStream models temporal dynamics using hybrid durative actions, which can be started asynchronously and persist for a duration that's a function of their parameters. We propose domain-independent algorithms that solve ScheduleStream problems without any application-specific mechanisms. We apply ScheduleStream to Task and Motion Planning & Scheduling (TAMPAS), where we use GPU acceleration within samplers to expedite planning. We compare ScheduleStream algorithms to several ablations in simulation and find that they produce more efficient solutions. We demonstrate ScheduleStream on several real-world bimanual robot tasks at https://schedulestream.github.io.

Qi Chen, Fabio Ramos, Alán Aspuru-Guzik et al.

Bayesian Optimization (BO) is a key methodology for accelerating molecular discovery by estimating the mapping from molecules to their properties while seeking the optimal candidate. Typically, BO iteratively updates a probabilistic surrogate model of this mapping and optimizes acquisition functions derived from the model to guide molecule selection. However, its performance is limited in low-data regimes with insufficient prior knowledge and vast candidate spaces. Large language models (LLMs) and chemistry foundation models offer rich priors to enhance BO, but high-dimensional features, costly in-context learning, and the computational burden of deep Bayesian surrogates hinder their full utilization. To address these challenges, we propose a likelihood-free BO method that bypasses explicit surrogate modeling and directly leverages priors from general LLMs and chemistry-specific foundation models to inform acquisition functions. Our method also learns a tree-structured partition of the molecular search space with local acquisition functions, enabling efficient candidate selection via Monte Carlo Tree Search. By further incorporating coarse-grained LLM-based clustering, it substantially improves scalability to large candidate sets by restricting acquisition function evaluations to clusters with statistically higher property values. We show through extensive experiments and ablations that the proposed method substantially improves scalability, robustness, and sample efficiency in LLM-guided BO for molecular discovery.

Mohak Bhardwaj, Balakumar Sundaralingam, Arsalan Mousavian et al.

Sampling-based model-predictive control (MPC) is a promising tool for feedback control of robots with complex, non-smooth dynamics, and cost functions. However, the computationally demanding nature of sampling-based MPC algorithms has been a key bottleneck in their application to high-dimensional robotic manipulation problems in the real world. Previous methods have addressed this issue by running MPC in the task space while relying on a low-level operational space controller for joint control. However, by not using the joint space of the robot in the MPC formulation, existing methods cannot directly account for non-task space related constraints such as avoiding joint limits, singular configurations, and link collisions. In this paper, we develop a system for fast, joint space sampling-based MPC for manipulators that is efficiently parallelized using GPUs. Our approach can handle task and joint space constraints while taking less than 8ms~(125Hz) to compute the next control command. Further, our method can tightly integrate perception into the control problem by utilizing learned cost functions from raw sensor data. We validate our approach by deploying it on a Franka Panda robot for a variety of dynamic manipulation tasks. We study the effect of different cost formulations and MPC parameters on the synthesized behavior and provide key insights that pave the way for the application of sampling-based MPC for manipulators in a principled manner. We also provide highly optimized, open-source code to be used by the wider robot learning and control community. Videos of experiments can be found at: https://sites.google.com/view/manipulation-mpc

Bhairav Mehta, Ankur Handa, Dieter Fox et al.

Simulators are a critical component of modern robotics research. Strategies for both perception and decision making can be studied in simulation first before deployed to real world systems, saving on time and costs. Despite significant progress on the development of sim-to-real algorithms, the analysis of different methods is still conducted in an ad-hoc manner, without a consistent set of tests and metrics for comparison. This paper fills this gap and proposes a set of benchmarks and a framework for the study of various algorithms aimed to transfer models and policies learnt in simulation to the real world. We conduct experiments on a wide range of well known simulated environments to characterize and offer insights into the performance of different algorithms. Our analysis can be useful for practitioners working in this area and can help make informed choices about the behavior and main properties of sim-to-real algorithms. We open-source the benchmark, training data, and trained models, which can be found at https://github.com/NVlabs/sim-parameter-estimation.

Yi Li, Yuquan Deng, Jesse Zhang et al. · mit, nvidia

Large foundation models have shown strong open-world generalization to complex problems in vision and language, but similar levels of generalization have yet to be achieved in robotics. One fundamental challenge is the lack of robotic data, which are typically obtained through expensive on-robot operation. A promising remedy is to leverage cheaper, off-domain data such as action-free videos, hand-drawn sketches or simulation data. In this work, we posit that hierarchical vision-language-action (VLA) models can be more effective in utilizing off-domain data than standard monolithic VLA models that directly finetune vision-language models (VLMs) to predict actions. In particular, we study a class of hierarchical VLA models, where the high-level VLM is finetuned to produce a coarse 2D path indicating the desired robot end-effector trajectory given an RGB image and a task description. The intermediate 2D path prediction is then served as guidance to the low-level, 3D-aware control policy capable of precise manipulation. Doing so alleviates the high-level VLM from fine-grained action prediction, while reducing the low-level policy's burden on complex task-level reasoning. We show that, with the hierarchical design, the high-level VLM can transfer across significant domain gaps between the off-domain finetuning data and real-robot testing scenarios, including differences on embodiments, dynamics, visual appearances and task semantics, etc. In the real-robot experiments, we observe an average of 20% improvement in success rate across seven different axes of generalization over OpenVLA, representing a 50% relative gain. Visual results, code, and dataset are provided at: https://hamster-robot.github.io/

Motoya Ohnishi, Iretiayo Akinola, Jie Xu et al.

Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor products. Signatures have recently been widely adopted in machine learning problems for time series analysis. In this work we establish connections between value functions typically used in optimal control and intriguing properties of path signatures. These connections motivate our novel control framework with signature transforms that efficiently generalizes the Bellman equation to the space of trajectories. We analyze the properties and advantages of the framework, termed signature control. In particular, we demonstrate that (i) it can naturally deal with varying/adaptive time steps; (ii) it propagates higher-level information more efficiently than value function updates; (iii) it is robust to dynamical system misspecification over long rollouts. As a specific case of our framework, we devise a model predictive control method for path tracking. This method generalizes integral control, being suitable for problems with unknown disturbances. The proposed algorithms are tested in simulation, with differentiable physics models including typical control and robotics tasks such as point-mass, curve following for an ant model, and a robotic manipulator.

Ankit Goyal, Hugo Hadfield, Xuning Yang et al. · nvidia

Vision-Language-Action models (VLAs) hold immense promise for enabling generalist robot manipulation. However, the best way to build them remains an open question. Current approaches often add complexity, such as modifying the existing vocabulary of a Vision-Language Model (VLM) with action tokens or introducing special action heads. Curiously, the simplest strategy of representing actions directly as text has remained largely unexplored. This work introduces VLA-0 to investigate this idea. We find that VLA-0 is not only effective; it is surprisingly powerful. With the right design, VLA-0 outperforms more involved models. On LIBERO, a popular benchmark for evaluating VLAs, VLA-0 outperforms all existing methods trained on the same robotic data, including $π_0.5$-KI, OpenVLA-OFT and SmolVLA. Furthermore, without large-scale robotics-specific training, it outperforms methods trained on large-scale robotic data, like $π_0.5$-KI, $π_0$, GR00T-N1 and MolmoAct. These findings also translate to the real world, where VLA-0 outperforms SmolVLA, a VLA model pre-trained on large-scale real data. This paper summarizes our unexpected findings and spells out the specific techniques required to unlock the high performance of this simple yet potent VLA design. Visual results, code, and trained models are provided here: https://vla0.github.io/.

Elie Aljalbout, Jiaxu Xing, Angel Romero et al. · mit, nvidia

Machine learning has facilitated significant advancements across various robotics domains, including navigation, locomotion, and manipulation. Many such achievements have been driven by the extensive use of simulation as a critical tool for training and testing robotic systems prior to their deployment in real-world environments. However, simulations consist of abstractions and approximations that inevitably introduce discrepancies between simulated and real environments, known as the reality gap. These discrepancies significantly hinder the successful transfer of systems from simulation to the real world. Closing this gap remains one of the most pressing challenges in robotics. Recent advances in sim-to-real transfer have demonstrated promising results across various platforms, including locomotion, navigation, and manipulation. By leveraging techniques such as domain randomization, real-to-sim transfer, state and action abstractions, and sim-real co-training, many works have overcome the reality gap. However, challenges persist, and a deeper understanding of the reality gap's root causes and solutions is necessary. In this survey, we present a comprehensive overview of the sim-to-real landscape, highlighting the causes, solutions, and evaluation metrics for the reality gap and sim-to-real transfer.

Yilin Wu, Anqi Li, Tucker Hermans et al. · nvidia

Reasoning Vision Language Action (VLA) models improve robotic instruction-following by generating step-by-step textual plans before low-level actions, an approach inspired by Chain-of-Thought (CoT) reasoning in language models. Yet even with a correct textual plan, the generated actions can still miss the intended outcomes in the plan, especially in out-of-distribution (OOD) scenarios. We formalize this phenomenon as a lack of embodied CoT faithfulness, and introduce a training-free, runtime policy steering method for reasoning-action alignment. Given a reasoning VLA's intermediate textual plan, our framework samples multiple candidate action sequences from the same model, predicts their outcomes via simulation, and uses a pre-trained Vision-Language Model (VLM) to select the sequence whose outcome best aligns with the VLA's own textual plan. Only executing action sequences that align with the textual reasoning turns our base VLA's natural action diversity from a source of error into a strength, boosting robustness to semantic and visual OOD perturbations and enabling novel behavior composition without costly re-training. We also contribute a reasoning-annotated extension of LIBERO-100, environment variations tailored for OOD evaluation, and demonstrate up to 15% performance gain over prior work on behavior composition tasks and scales with compute and data diversity. Project Website at: https://yilin-wu98.github.io/steering-reasoning-vla/

Kim Bente, Roman Marchant, Fabio Ramos

To reliably project future sea level rise, ice sheet models require inputs that respect physics. Embedding physical principles like mass conservation into models that interpolate Antarctic ice flow vector fields from sparse & noisy measurements not only promotes physical adherence but can also improve accuracy and robustness. While physics-informed neural networks (PINNs) impose physics as soft penalties, offering flexibility but no physical guarantees, we instead propose divergence-free neural networks (dfNNs), which enforce local mass conservation exactly via a vector calculus trick. Our comparison of dfNNs, PINNs, and unconstrained NNs on ice flux interpolation over Byrd Glacier suggests that "mass conservation on rails" yields more reliable estimates, and that directional guidance, a learning strategy leveraging continent-wide satellite velocity data, boosts performance across models.

Jesse Zhang, Marius Memmel, Kevin Kim et al.

Robotic manipulation policies often fail to generalize because they must simultaneously learn where to attend, what actions to take, and how to execute them. We argue that high-level reasoning about where and what can be offloaded to vision-language models (VLMs), leaving policies to specialize in how to act. We present PEEK (Policy-agnostic Extraction of Essential Keypoints), which fine-tunes VLMs to predict a unified point-based intermediate representation: 1. end-effector paths specifying what actions to take, and 2. task-relevant masks indicating where to focus. These annotations are directly overlaid onto robot observations, making the representation policy-agnostic and transferable across architectures. To enable scalable training, we introduce an automatic annotation pipeline, generating labeled data across 20+ robot datasets spanning 9 embodiments. In real-world evaluations, PEEK consistently boosts zero-shot generalization, including a 41.4x real-world improvement for a 3D policy trained only in simulation, and 2-3.5x gains for both large VLAs and small manipulation policies. By letting VLMs absorb semantic and visual complexity, PEEK equips manipulation policies with the minimal cues they need--where, what, and how. Website at https://peek-robot.github.io/.

Jayadeep Jacob, Wenzheng Zhang, Houston Warren et al.

Manipulating clusters of deformable objects presents a substantial challenge with widespread applicability, but requires contact-rich whole-arm interactions. A potential solution must address the limited capacity for realistic model synthesis, high uncertainty in perception, and the lack of efficient spatial abstractions, among others. We propose a novel framework for learning model-free policies integrating two modalities: 3D point clouds and proprioceptive touch indicators, emphasising manipulation with full body contact awareness, going beyond traditional end-effector modes. Our reinforcement learning framework leverages a distributional state representation, aided by kernel mean embeddings, to achieve improved training efficiency and real-time inference. Furthermore, we propose a novel context-agnostic occlusion heuristic to clear deformables from a target region for exposure tasks. We deploy the framework in a power line clearance scenario and observe that the agent generates creative strategies leveraging multiple arm links for de-occlusion. Finally, we perform zero-shot sim-to-real policy transfer, allowing the arm to clear real branches with unknown occlusion patterns, unseen topology, and uncertain dynamics.

Shizhe Cai, Jayadeep Jacob, Zeya Yin et al.

Deep reinforcement learning has shown remarkable success in continuous control tasks, yet often requires extensive training data, struggles with complex, long-horizon planning, and fails to maintain safety constraints during operation. Meanwhile, Model Predictive Control (MPC) offers explainability and constraint satisfaction, but typically yields only locally optimal solutions and demands careful cost function design. This paper introduces the Q-guided STein variational model predictive Actor-Critic (Q-STAC), a novel framework that bridges these approaches by integrating Bayesian MPC with actor-critic reinforcement learning through constrained Stein Variational Gradient Descent (SVGD). Our method optimizes control sequences directly using learned Q-values as objectives, eliminating the need for explicit cost function design while leveraging known system dynamics to enhance sample efficiency and ensure control signals remain within safe boundaries. Extensive experiments on 2D navigation and robotic manipulation tasks demonstrate that Q-STAC achieves superior sample efficiency, robustness, and optimality compared to state-of-the-art algorithms, while maintaining the high expressiveness of policy distributions. Experiment videos are available on our website: https://sites.google.com/view/q-stac

Houston Warren, Rafael Oliveira, Fabio Ramos

In large-scale regression problems, random Fourier features (RFFs) have significantly enhanced the computational scalability and flexibility of Gaussian processes (GPs) by defining kernels through their spectral density, from which a finite set of Monte Carlo samples can be used to form an approximate low-rank GP. However, the efficacy of RFFs in kernel approximation and Bayesian kernel learning depends on the ability to tractably sample the kernel spectral measure and the quality of the generated samples. We introduce Stein random features (SRF), leveraging Stein variational gradient descent, which can be used to both generate high-quality RFF samples of known spectral densities as well as flexibly and efficiently approximate traditionally non-analytical spectral measure posteriors. SRFs require only the evaluation of log-probability gradients to perform both kernel approximation and Bayesian kernel learning that results in superior performance over traditional approaches. We empirically validate the effectiveness of SRFs by comparing them to baselines on kernel approximation and well-known GP regression problems.

Fahira Afzal Maken, Fabio Ramos, Lionel Ott

Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and Gaussian noise problems, the general nonlinear and non-Gaussian noise case is significantly more complicated, typically relying on sampling strategies that are limited to low-dimensional state spaces. In this paper we devise a general inference procedure for filtering of nonlinear, non-Gaussian dynamical systems that exploits the differentiability of both the update and prediction models to scale to higher dimensional spaces. Our method, Stein particle filter, can be seen as a deterministic flow of particles, embedded in a reproducing kernel Hilbert space, from an initial state to the desirable posterior. The particles evolve jointly to conform to a posterior approximation while interacting with each other through a repulsive force. We evaluate the method in simulation and in complex localization tasks while comparing it to sequential Monte Carlo solutions.

Rika Antonova, Jingyun Yang, Priya Sundaresan et al.

Deformable object manipulation remains a challenging task in robotics research. Conventional techniques for parameter inference and state estimation typically rely on a precise definition of the state space and its dynamics. While this is appropriate for rigid objects and robot states, it is challenging to define the state space of a deformable object and how it evolves in time. In this work, we pose the problem of inferring physical parameters of deformable objects as a probabilistic inference task defined with a simulator. We propose a novel methodology for extracting state information from image sequences via a technique to represent the state of a deformable object as a distribution embedding. This allows to incorporate noisy state observations directly into modern Bayesian simulation-based inference tools in a principled manner. Our experiments confirm that we can estimate posterior distributions of physical properties, such as elasticity, friction and scale of highly deformable objects, such as cloth and ropes. Overall, our method addresses the real-to-sim problem probabilistically and helps to better represent the evolution of the state of deformable objects.

Fabio Muratore, Fabio Ramos, Greg Turk et al.

The rise of deep learning has caused a paradigm shift in robotics research, favoring methods that require large amounts of data. Unfortunately, it is prohibitively expensive to generate such data sets on a physical platform. Therefore, state-of-the-art approaches learn in simulation where data generation is fast as well as inexpensive and subsequently transfer the knowledge to the real robot (sim-to-real). Despite becoming increasingly realistic, all simulators are by construction based on models, hence inevitably imperfect. This raises the question of how simulators can be modified to facilitate learning robot control policies and overcome the mismatch between simulation and reality, often called the 'reality gap'. We provide a comprehensive review of sim-to-real research for robotics, focusing on a technique named 'domain randomization' which is a method for learning from randomized simulations.

Tin Lai, Fabio Ramos

In an environment where a manipulator needs to execute multiple consecutive tasks, the act of object manoeuvre will change the underlying configuration space, affecting all subsequent tasks. Previously free configurations might now be occupied by the manoeuvred objects, and previously occupied space might now open up new paths. We propose Lazy Tree-based Replanner (LTR*) -- a novel hybrid planner that inherits the rapid planning nature of existing anytime incremental sampling-based planners. At the same time, it allows subsequent tasks to leverage prior experience via a lazy experience graph. Previous experience is summarised in a lazy graph structure, and LTR* is formulated to be robust and beneficial regardless of the extent of changes in the workspace. Our hybrid approach attains a faster speed in obtaining an initial solution than existing roadmap-based planners and often with a lower cost in trajectory length. Subsequent tasks can utilise the lazy experience graph to speed up finding a solution and take advantage of the optimised graph to minimise the cost objective. We provide proofs of probabilistic completeness and almost-surely asymptotic optimal guarantees. Experimentally, we show that in repeated pick-and-place tasks, LTR* attains a high gain in performance when planning for subsequent tasks.

Eric Heiden, Christopher E. Denniston, David Millard et al.

To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through a Bayesian inference approach that approximates a posterior distribution over simulation parameters given real sensor measurements. By extending the commonly used Gaussian likelihood model for trajectories via the multiple-shooting formulation, our chosen particle-based inference algorithm Stein Variational Gradient Descent is able to identify highly nonlinear, underactuated systems. We leverage GPU code generation and differentiable simulation to evaluate the likelihood and its gradient for many particles in parallel. Our algorithm infers non-parametric distributions over simulation parameters more accurately than comparable baselines and handles constraints over parameters efficiently through gradient-based optimization. We evaluate estimation performance on several physical experiments. On an underactuated mechanism where a 7-DOF robot arm excites an object with an unknown mass configuration, we demonstrate how our inference technique can identify symmetries between the parameters and provide highly accurate predictions. Project website: https://uscresl.github.io/prob-diff-sim

Tin Lai, Weiming Zhi, Tucker Hermans et al.

We propose Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP). PDMP is a novel parallelised framework that uses bijective and differentiable mappings, or diffeomorphisms, to transform sampling distributions of sampling-based motion planners, in a manner akin to normalising flows. Unlike normalising flow models which use invertible neural network structures to represent these diffeomorphisms, we develop them from gradient information of desired costs, and encode desirable behaviour, such as obstacle avoidance. These transformed sampling distributions can then be used for sampling-based motion planning. A particular example is when we wish to imbue the sampling distribution with knowledge of the environment geometry, such that drawn samples are less prone to be in collisions. To this end, we propose to learn a continuous occupancy representation from environment occupancy data, such that gradients of the representation defines a valid diffeomorphism and is amenable to fast parallel evaluation. We use this to "morph" the sampling distribution to draw far fewer collision-prone samples. PDMP is able to leverage gradient information of costs, to inject specifications, in a manner similar to optimisation-based motion planning methods, but relies on drawing from a sampling distribution, retaining the tendency to find more global solutions, thereby bridging the gap between trajectory optimisation and sampling-based planning methods.

Rika Antonova, Fabio Ramos, Rafael Possas et al.

BayesSim is a statistical technique for domain randomization in reinforcement learning based on likelihood-free inference of simulation parameters. This paper outlines BayesSimIG: a library that provides an implementation of BayesSim integrated with the recently released NVIDIA IsaacGym. This combination allows large-scale parameter inference with end-to-end GPU acceleration. Both inference and simulation get GPU speedup, with support for running more than 10K parallel simulation environments for complex robotics tasks that can have more than 100 simulation parameters to estimate. BayesSimIG provides an integration with TensorBoard to easily visualize slices of high-dimensional posteriors. The library is built in a modular way to support research experiments with novel ways to collect and process the trajectories from the parallel IsaacGym environments.

Weiming Zhi, Lionel Ott, Fabio Ramos

This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from observed trajectories, with no mechanism to directly incorporate known rules. We propose a novel framework, which combines probabilistic learning and constrained trajectory optimisation. The learning component of our framework provides a distribution over future motion trajectories conditioned on observed past coordinates. This distribution is then used as a prior to a constrained optimisation problem which enforces chance constraints on the trajectory distribution. This results in constraint-compliant trajectory distributions which closely resemble the prior. In particular, we focus our investigation on collision constraints, such that extrapolated future trajectory distributions conform to the environment structure. We empirically demonstrate on real-world and simulated datasets the ability of our framework to learn complex probabilistic motion trajectories for motion data, while directly enforcing constraints to improve generalisability, producing more robust and higher quality trajectory distributions.

Weiming Zhi, Tin Lai, Lionel Ott et al.

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs (NODEs), a class of deep learning models with continuous depth, rather than discrete layers. However, these integrators can be unsatisfactorily slow and inaccurate when learning systems of ODEs from long sequences, or when solutions of the system vary at widely different timescales in each dimension. In this paper we propose an alternative approach to learning ODEs from data: we represent the underlying ODE as a vector field that is related to another base vector field by a differentiable bijection, modelled by an invertible neural network. By restricting the base ODE to be amenable to integration, we can drastically speed up and improve the robustness of integration. We demonstrate the efficacy of our method in training and evaluating continuous neural networks models, as well as in learning benchmark ODE systems. We observe improvements of up to two orders of magnitude when integrating learned ODEs with GPUs computation.

Fahira Afzal Maken, Fabio Ramos, Lionel Ott

Quantification of uncertainty in point cloud matching is critical in many tasks such as pose estimation, sensor fusion, and grasping. Iterative closest point (ICP) is a commonly used pose estimation algorithm which provides a point estimate of the transformation between two point clouds. There are many sources of uncertainty in this process that may arise due to sensor noise, ambiguous environment, and occlusion. However, for safety critical problems such as autonomous driving, a point estimate of the pose transformation is not sufficient as it does not provide information about the multiple solutions. Current probabilistic ICP methods usually do not capture all sources of uncertainty and may provide unreliable transformation estimates which can have a detrimental effect in state estimation or decision making tasks that use this information. In this work we propose a new algorithm to align two point clouds that can precisely estimate the uncertainty of ICP's transformation parameters. We develop a Stein variational inference framework with gradient based optimization of ICP's cost function. The method provides a non-parametric estimate of the transformation, can model complex multi-modal distributions, and can be effectively parallelized on a GPU. Experiments using 3D kinect data as well as sparse indoor/outdoor LiDAR data show that our method is capable of efficiently producing accurate pose uncertainty estimates.

Eric Heiden, Miles Macklin, Yashraj Narang et al.

Robotic cutting of soft materials is critical for applications such as food processing, household automation, and surgical manipulation. As in other areas of robotics, simulators can facilitate controller verification, policy learning, and dataset generation. Moreover, differentiable simulators can enable gradient-based optimization, which is invaluable for calibrating simulation parameters and optimizing controllers. In this work, we present DiSECt: the first differentiable simulator for cutting soft materials. The simulator augments the finite element method (FEM) with a continuous contact model based on signed distance fields (SDF), as well as a continuous damage model that inserts springs on opposite sides of the cutting plane and allows them to weaken until zero stiffness, enabling crack formation. Through various experiments, we evaluate the performance of the simulator. We first show that the simulator can be calibrated to match resultant forces and deformation fields from a state-of-the-art commercial solver and real-world cutting datasets, with generality across cutting velocities and object instances. We then show that Bayesian inference can be performed efficiently by leveraging the differentiability of the simulator, estimating posteriors over hundreds of parameters in a fraction of the time of derivative-free methods. Finally, we illustrate that control parameters in the simulation can be optimized to minimize cutting forces via lateral slicing motions. We publish videos and additional results on our project website at https://diff-cutting-sim.github.io.

Lucas Barcelos, Alexander Lambert, Rafael Oliveira et al.

Model predictive control (MPC) schemes have a proven track record for delivering aggressive and robust performance in many challenging control tasks, coping with nonlinear system dynamics, constraints, and observational noise. Despite their success, these methods often rely on simple control distributions, which can limit their performance in highly uncertain and complex environments. MPC frameworks must be able to accommodate changing distributions over system parameters, based on the most recent measurements. In this paper, we devise an implicit variational inference algorithm able to estimate distributions over model parameters and control inputs on-the-fly. The method incorporates Stein Variational gradient descent to approximate the target distributions as a collection of particles, and performs updates based on a Bayesian formulation. This enables the approximation of complex multi-modal posterior distributions, typically occurring in challenging and realistic robot navigation tasks. We demonstrate our approach on both simulated and real-world experiments requiring real-time execution in the face of dynamically changing environments.

Louis C. Tiao, Aaron Klein, Matthias Seeger et al.

Bayesian optimization (BO) is among the most effective and widely-used blackbox optimization methods. BO proposes solutions according to an explore-exploit trade-off criterion encoded in an acquisition function, many of which are computed from the posterior predictive of a probabilistic surrogate model. Prevalent among these is the expected improvement (EI) function. The need to ensure analytical tractability of the predictive often poses limitations that can hinder the efficiency and applicability of BO. In this paper, we cast the computation of EI as a binary classification problem, building on the link between class-probability estimation and density-ratio estimation, and the lesser-known link between density-ratios and EI. By circumventing the tractability constraints, this reformulation provides numerous advantages, not least in terms of expressiveness, versatility, and scalability.

Guanya Shi, Yifeng Zhu, Jonathan Tremblay et al.

Deep learning-based object pose estimators are often unreliable and overconfident especially when the input image is outside the training domain, for instance, with sim2real transfer. Efficient and robust uncertainty quantification (UQ) in pose estimators is critically needed in many robotic tasks. In this work, we propose a simple, efficient, and plug-and-play UQ method for 6-DoF object pose estimation. We ensemble 2-3 pre-trained models with different neural network architectures and/or training data sources, and compute their average pairwise disagreement against one another to obtain the uncertainty quantification. We propose four disagreement metrics, including a learned metric, and show that the average distance (ADD) is the best learning-free metric and it is only slightly worse than the learned metric, which requires labeled target data. Our method has several advantages compared to the prior art: 1) our method does not require any modification of the training process or the model inputs; and 2) it needs only one forward pass for each model. We evaluate the proposed UQ method on three tasks where our uncertainty quantification yields much stronger correlations with pose estimation errors than the baselines. Moreover, in a real robot grasping task, our method increases the grasping success rate from 35% to 90%.

Alexander Lambert, Adam Fishman, Dieter Fox et al.

Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex probability distributions. In this paper, we propose a generalization of MPC that represents a multitude of solutions as posterior distributions. By casting MPC as a Bayesian inference problem, we employ variational methods for posterior computation, naturally encoding the complexity and multi-modality of the decision making problem. We present a Stein variational gradient descent method to estimate the posterior directly over control parameters, given a cost function and observed state trajectories. We show that this framework leads to successful planning in challenging, non-convex optimal control problems.

Weiming Zhi, Tin Lai, Lionel Ott et al.

Critical for the coexistence of humans and robots in dynamic environments is the capability for agents to understand each other's actions, and anticipate their movements. This paper presents Stochastic Process Anticipatory Navigation (SPAN), a framework that enables nonholonomic robots to navigate in environments with crowds, while anticipating and accounting for the motion patterns of pedestrians. To this end, we learn a predictive model to predict continuous-time stochastic processes to model future movement of pedestrians. Anticipated pedestrian positions are used to conduct chance constrained collision-checking, and are incorporated into a time-to-collision control problem. An occupancy map is also integrated to allow for probabilistic collision-checking with static obstacles. We demonstrate the capability of SPAN in crowded simulation environments, as well as with a real-world pedestrian dataset.

Carolyn Matl, Yashraj Narang, Dieter Fox et al.

Sound is an information-rich medium that captures dynamic physical events. This work presents STReSSD, a framework that uses sound to bridge the simulation-to-reality gap for stochastic dynamics, demonstrated for the canonical case of a bouncing ball. A physically-motivated noise model is presented to capture stochastic behavior of the balls upon collision with the environment. A likelihood-free Bayesian inference framework is used to infer the parameters of the noise model, as well as a material property called the coefficient of restitution, from audio observations. The same inference framework and the calibrated stochastic simulator are then used to learn a probabilistic model of ball dynamics. The predictive capabilities of the dynamics model are tested in two robotic experiments. First, open-loop predictions anticipate probabilistic success of bouncing a ball into a cup. The second experiment integrates audio perception with a robotic arm to track and deflect a bouncing ball in real-time. We envision that this work is a step towards integrating audio-based inference for dynamic robotic tasks. Experimental results can be viewed at https://youtu.be/b7pOrgZrArk.

Tin Lai, Fabio Ramos

Sampling-based motion planning is the predominant paradigm in many real-world robotic applications, but its performance is immensely dependent on the quality of the samples. The majority of traditional planners are inefficient as they use uninformative sampling distributions as opposed to exploiting structures and patterns in the problem to guide better sampling strategies. Moreover, most current learning-based planners are susceptible to posterior collapse or mode collapse due to the sparsity and highly varying nature of C-Space and motion plan configurations. In this work, we introduce a conditional normalising flow based distribution learned through previous experiences to improve sampling of these methods. Our distribution can be conditioned on the current problem instance to provide an informative prior for sampling configurations within promising regions. When we train our sampler with an expert planner, the resulting distribution is often near-optimal, and the planner can find a solution faster, with less invalid samples, and less initial cost. The normalising flow based distribution uses simple invertible transformations that are very computationally efficient, and our optimisation formulation explicitly avoids mode collapse in contrast to other existing learning-based planners. Finally, we provide a formulation and theoretical foundation to efficiently sample from the distribution; and demonstrate experimentally that, by using our normalising flow based distribution, a solution can be found faster, with less samples and better overall runtime performance.

Sebastian Haan, Fabio Ramos, Dietmar Müller

A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and to minimize total cost. We propose a probabilistic framework for multi-objective optimisation and inverse problems given an expensive cost function for allocating new measurements. This new method is devised to jointly solve multi-linear forward models of 2D-sensor data and 3D-geophysical properties using sparse Gaussian Process kernels while taking into account the cross-variances of different parameters. Multiple optimisation strategies are tested and evaluated on a set of synthetic and real geophysical data. We demonstrate the advantages on a specific example of a joint inverse problem, recommending where to place new drill-core measurements given 2D gravity and magnetic sensor data, the same approach can be applied to a variety of remote sensing problems with linear forward models - ranging from constraints limiting surface access for data acquisition to adaptive multi-sensor positioning.

Anthony Tompkins, Rafael Oliveira, Fabio Ramos

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness with respect to the input. The proposed learning algorithm warps inputs as conditional Gaussian measures that control the smoothness of a standard stationary kernel. This construction allows us to capture non-stationary patterns in the data and provides intuitive inductive bias. The resulting method is based on sparse spectrum Gaussian processes, enabling closed-form solutions, and is extensible to a stacked construction to capture more complex patterns. The method is extensively validated alongside related algorithms on synthetic and real world datasets. We demonstrate a remarkable efficiency in the number of parameters of the warping functions in learning problems with both small and large data regimes.

Rel Guzman, Rafael Oliveira, Fabio Ramos

Model predictive control (MPC) has been successful in applications involving the control of complex physical systems. This class of controllers leverages the information provided by an approximate model of the system's dynamics to simulate the effect of control actions. MPC methods also present a few hyper-parameters which may require a relatively expensive tuning process by demanding interactions with the physical system. Therefore, we investigate fine-tuning MPC methods in the context of stochastic MPC, which presents extra challenges due to the randomness of the controller's actions. In these scenarios, performance outcomes present noise, which is not homogeneous across the domain of possible hyper-parameter settings, but which varies in an input-dependent way. To address these issues, we propose a Bayesian optimisation framework that accounts for heteroscedastic noise to tune hyper-parameters in control problems. Empirical results on benchmark continuous control tasks and a physical robot support the proposed framework's suitability relative to baselines, which do not take heteroscedasticity into account.

Anthony Tompkins, Ransalu Senanayake, Fabio Ramos

Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy maps, learning the parameters of such models demand considerable computational time, discouraging them from being used in real-time and large-scale applications such as autonomous driving. Recognizing the fact that real-world structures exhibit similar geometric features across a variety of urban environments, in this paper, we argue that it is redundant to learn all geometry dependent parameters from scratch. Instead, we propose a theoretical framework building upon the theory of optimal transport to adapt model parameters to account for changes in the environment, significantly amortizing the training cost. Further, with the use of high-fidelity driving simulators and real-world datasets, we demonstrate how parameters of 2D and 3D occupancy maps can be automatically adapted to accord with local spatial changes. We validate various domain adaptation paradigms through a series of experiments, ranging from inter-domain feature transfer to simulation-to-real-world feature transfer. Experiments verified the possibility of estimating parameters with a negligible computational and memory cost, enabling large-scale probabilistic mapping in urban environments.

Muhammad Asif Rana, Anqi Li, Dieter Fox et al.

Robotic tasks often require motions with complex geometric structures. We present an approach to learn such motions from a limited number of human demonstrations by exploiting the regularity properties of human motions e.g. stability, smoothness, and boundedness. The complex motions are encoded as rollouts of a stable dynamical system, which, under a change of coordinates defined by a diffeomorphism, is equivalent to a simple, hand-specified dynamical system. As an immediate result of using diffeomorphisms, the stability property of the hand-specified dynamical system directly carry over to the learned dynamical system. Inspired by recent works in density estimation, we propose to represent the diffeomorphism as a composition of simple parameterized diffeomorphisms. Additional structure is imposed to provide guarantees on the smoothness of the generated motions. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.

Michelle A. Lee, Carlos Florensa, Jonathan Tremblay et al.

Traditional robotic approaches rely on an accurate model of the environment, a detailed description of how to perform the task, and a robust perception system to keep track of the current state. On the other hand, reinforcement learning approaches can operate directly from raw sensory inputs with only a reward signal to describe the task, but are extremely sample-inefficient and brittle. In this work, we combine the strengths of model-based methods with the flexibility of learning-based methods to obtain a general method that is able to overcome inaccuracies in the robotics perception/actuation pipeline, while requiring minimal interactions with the environment. This is achieved by leveraging uncertainty estimates to divide the space in regions where the given model-based policy is reliable, and regions where it may have flaws or not be well defined. In these uncertain regions, we show that a locally learned-policy can be used directly with raw sensory inputs. We test our algorithm, Guided Uncertainty-Aware Policy Optimization (GUAPO), on a real-world robot performing peg insertion. Videos are available at https://sites.google.com/view/guapo-rl

Fahira Afzal Maken, Fabio Ramos, Lionel Ott

Accurate uncertainty estimation associated with the pose transformation between two 3D point clouds is critical for autonomous navigation, grasping, and data fusion. Iterative closest point (ICP) is widely used to estimate the transformation between point cloud pairs by iteratively performing data association and motion estimation. Despite its success and popularity, ICP is effectively a deterministic algorithm, and attempts to reformulate it in a probabilistic manner generally do not capture all sources of uncertainty, such as data association errors and sensor noise. This leads to overconfident transformation estimates, potentially compromising the robustness of systems relying on them. In this paper we propose a novel method to estimate pose uncertainty in ICP with a Markov Chain Monte Carlo (MCMC) algorithm. Our method combines recent developments in optimization for scalable Bayesian sampling such as stochastic gradient Langevin dynamics (SGLD) to infer a full posterior distribution of the pose transformation between two point clouds. We evaluate our method, called Bayesian ICP, in experiments using 3D Kinect data demonstrating that our method is capable of both quickly and accuractely estimating pose uncertainty, taking into account data association uncertainty as reflected by the shape of the objects.

Philippe Morere, Fabio Ramos

Intrinsic motivation enables reinforcement learning (RL) agents to explore when rewards are very sparse, where traditional exploration heuristics such as Boltzmann or e-greedy would typically fail. However, intrinsic exploration is generally handled in an ad-hoc manner, where exploration is not treated as a core objective of the learning process; this weak formulation leads to sub-optimal exploration performance. To overcome this problem, we propose a framework based on multi-objective RL where both exploration and exploitation are being optimized as separate objectives. This formulation brings the balance between exploration and exploitation at a policy level, resulting in advantages over traditional methods. This also allows for controlling exploration while learning, at no extra cost. Such strategies achieve a degree of control over agent exploration that was previously unattainable with classic or intrinsic rewards. We demonstrate scalability to continuous state-action spaces by presenting a method (EMU-Q) based on our framework, guiding exploration towards regions of higher value-function uncertainty. EMU-Q is experimentally shown to outperform classic exploration techniques and other intrinsic RL methods on a continuous control benchmark and on a robotic manipulator.