Vince Kurtz

Vince Kurtz, Hai Lin

Contact-implicit trajectory optimization offers an appealing method of automatically generating complex and contact-rich behaviors for robot manipulation and locomotion. The scalability of such techniques has been limited, however, by the challenge of ensuring both numerical reliability and physical realism. In this paper, we present preliminary results suggesting that the Iterative Linear Quadratic Regulator (iLQR) algorithm together with the recently proposed pressure-field-based hydroelastic contact model enables reliable and physically realistic trajectory optimization through contact. We use this approach to synthesize contact-rich behaviors like quadruped locomotion and whole-arm manipulation. Furthermore, open-loop playback on a Kinova Gen3 robot arm demonstrates the physical accuracy of the whole-arm manipulation trajectories. Code is available at https://bit.ly/ilqr_hc and videos can be found at https://youtu.be/IqxJKbM8_ms.

Sergio A. Esteban, Junheng Li, Vince Kurtz et al.

Domain randomization (DR) is widely used in policy learning to improve robustness to modeling error, but remains underexplored in contact-rich sampling-based predictive control (SPC), where rollout quality is highly sensitive to uncertainty. In this work, we take the first step by studying risk-aware DR in predictive sampling on a simple yet representative Push-T task, comparing average, optimistic, and pessimistic rollout aggregations under randomized model instances. Our initial results suggest that DR affects not only robustness to model error, but also the effective cost landscape seen by the sampling-based optimizer, by reshaping the basin of attraction around contact-producing actions. This opens up potential for exploring better grounded risk-aware contact-rich SPC under model uncertainty. Video: https://youtu.be/f1F0ALXxhSM

Vince Kurtz, Joel W. Burdick

Generative control policies have recently unlocked major progress in robotics. These methods produce action sequences via diffusion or flow matching, with training data provided by demonstrations. But existing methods come with two key limitations: they require expert demonstrations, which can be difficult to obtain, and they are limited to relatively slow, quasi-static tasks. In this paper, we leverage a tight connection between sampling-based predictive control and generative modeling to address each of these issues. In particular, we introduce generative predictive control, a supervised learning framework for tasks with fast dynamics that are easy to simulate but difficult to demonstrate. We then show how trained flow-matching policies can be warm-started at inference time, maintaining temporal consistency and enabling high-frequency feedback. We believe that generative predictive control offers a complementary approach to existing behavior cloning methods, and hope that it paves the way toward generalist policies that extend beyond quasi-static demonstration-oriented tasks.

Rohan Thakker, Adarsh Patnaik, Vince Kurtz et al.

Safe, reliable navigation in extreme, unfamiliar terrain is required for future robotic space exploration missions. Recent generative-AI methods learn semantically aware navigation policies from large, cross-embodiment datasets, but offer limited safety guarantees. Inspired by human cognitive science, we propose a risk-guided diffusion framework that fuses a fast, learned "System-1" with a slow, physics-based "System-2", sharing computation at both training and inference to couple adaptability with formal safety. Hardware experiments conducted at the NASA JPL's Mars-analog facility, Mars Yard, show that our approach reduces failure rates by up to $4\times$ while matching the goal-reaching performance of learning-based robotic models by leveraging inference-time compute without any additional training.

Vince Kurtz, Patrick M. Wensing, Hai Lin

Task-space Passivity-Based Control (PBC) for manipulation has numerous appealing properties, including robustness to modeling error and safety for human-robot interaction. Existing methods perform poorly in singular configurations, however, such as when all the robot's joints are fully extended. Additionally, standard methods for constrained task-space PBC guarantee passivity only when constraints are not active. We propose a convex-optimization-based control scheme that provides guarantees of singularity avoidance, passivity, and feasibility. This work paves the way for PBC with passivity guarantees under other types of constraints as well, including joint limits and contact/friction constraints. The proposed methods are validated in simulation experiments on a 7 degree-of-freedom manipulator.

Vince Kurtz, He Li, Patrick M. Wensing et al.

Seemingly in defiance of basic physics, cats consistently land on their feet after falling. In this paper, we design a controller that lands the Mini Cheetah quadruped robot on its feet as well. Specifically, we explore how trajectory optimization and machine learning can work together to enable highly dynamic bioinspired behaviors. We find that a reflex approach, in which a neural network learns entire state trajectories, outperforms a policy approach, in which a neural network learns a mapping from states to control inputs. We validate our proposed controller in both simulation and hardware experiments, and are able to land the robot on its feet from falls with initial pitch angles between -90 and 90 degrees.

Vince Kurtz, Hai Lin

Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problem---generating a trajectory that satisfies a given specification---can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this letter, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.

Rafael Rodrigues da Silva, Vince Kurtz, Hai Lin

Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state-space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy non-convex \gls*{rtl} specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient boolean satisfiability (SAT) and \gls*{lp} solvers to find dynamically feasible trajectories that satisfy non-convex \gls*{rtl} specifications for high dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability.

Vince Kurtz, Patrick M. Wensing, Hai Lin

Reduced-order template models are widely used to control high degree-of-freedom legged robots, but existing methods for template-based whole-body control rely heavily on heuristics and often suffer from robustness issues. In this letter, we propose a template-based whole-body control method grounded in the formal framework of approximate simulation. Our central contribution is to demonstrate how the Hamiltonian structure of rigid-body dynamics can be exploited to establish approximate simulation for a high-dimensional nonlinear system. The resulting controller is passive, more robust to push disturbances, uneven terrain, and modeling errors than standard QP-based methods, and naturally enables high center of mass walking. Our theoretical results are supported by simulation experiments with a 30 degree-of-freedom Valkyrie humanoid model.

Yann Gilpin, Vince Kurtz, Hai Lin

Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as cost functions using STL's robust semantics, transforming the synthesis problem into an optimization problem. Unfortunately, these cost functions are non-smooth and non-convex, and exact solutions using mixed-integer programming do not scale well. Recent work has focused on using smooth approximations of robustness, which enable faster gradient-based methods to find local maxima, at the expense of soundness and/or completeness. We propose a novel robustness approximation that is smooth everywhere, sound, and asymptotically complete. Our approach combines the benefits of existing approximations, while enabling an explicit tradeoff between conservativeness and completeness.

Vince Kurtz, Hai Lin

Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet simple enough to enable efficient computation. We show that this model accurately reflects the measurement noise resulting from vision-based Simultaneous Localization and Mapping (SLAM), and argue that it provides a flexible means of modeling measurement noise for a wide variety of sensor systems and perception algorithms. We then extend existing results for Kalman filtering with autoregressive processes to more general Gaussian Processes, and demonstrate the improved performance of our approach.

Vince Kurtz, Rafael Rodrigues da Silva, Patrick M. Wensing et al.

Reduced-order template models like the Linear Inverted Pendulum (LIP) and Spring-Loaded Inverted Pendulum (SLIP) are widely used tools for controlling high-dimensional humanoid robots. However, connections between templates and whole-body models have lacked formal underpinnings, preventing formal guarantees when it comes to integrated controller design. We take a small step towards addressing this gap by considering the notion of approximate simulation. Derived from simulation relations for discrete transition systems in formal methods, approximate similarity means that the outputs of two systems can remain $ε$-close. In this paper, we consider the case of controlling a balancer via planning with the LIP model. We show that the balancer approximately simulates the LIP and derive linear constraints that are sufficient conditions for maintaining ground contact. This allows for rapid planning and replanning with the template model by solving a quadratic program that enforces contact constraints in the full model. We demonstrate the efficacy of this planning and control paradigm in a simulated push recovery scenario for a planar 4-link balancer.

Vince Kurtz, Hai Lin

In recent years, Signal Temporal Logic (STL) has gained traction as a practical and expressive means of encoding control objectives for robotic and cyber-physical systems. The state-of-the-art in STL trajectory synthesis is to formulate the problem as a Mixed Integer Linear Program (MILP). The MILP approach is sound and complete for bounded specifications, but such strong correctness guarantees come at the price of exponential complexity in the number of predicates and the time bound of the specification. In this work, we propose an alternative synthesis paradigm that relies on Bayesian optimization rather than mixed integer programming. This relaxes the completeness guarantee to probabilistic completeness, but is significantly more efficient: our approach scales polynomially in the STL time-bound and linearly in the number of predicates. We prove that our approach is sound and probabilistically complete, and demonstrate its scalability with a nontrivial example.

Rafael Rodrigues da Silva, Vince Kurtz, Hai Lin

Next-generation autonomous systems must execute complex tasks in uncertain environments. Active perception, where an autonomous agent selects actions to increase knowledge about the environment, has gained traction in recent years for motion planning under uncertainty. One prominent approach is planning in the belief space. However, most belief-space planning starts with a known reward function, which can be difficult to specify for complex tasks. On the other hand, symbolic control methods automatically synthesize controllers to achieve logical specifications, but often do not deal well with uncertainty. In this work, we propose a framework for scalable task and motion planning in uncertain environments that combines the best of belief-space planning and symbolic control. Specifically, we provide a counterexample-guided-inductive-synthesis algorithm for probabilistic temporal logic over reals (PRTL) specifications in the belief space. Our method automatically generates actions that improve confidence in a belief when necessary, thus using active perception to satisfy PRTL specifications.