arXiv subjects

Vince Kurtz

Publications and source records attributed to Vince Kurtz.

At least 19 recordsLinked to original sources

arXiv2026

Shooting for Contact: Contact-Implicit Multiple Shooting for Dynamic Motion Retargeting

Motion retargeting approaches often prioritize kinematic similarity over whole-body dynamics, contact consistency, and actuation limits, yielding references that are difficult for reinforcement learning (RL) policies to reproduce, particularly for contact-rich behaviors. We present a contact-implicit, direct simulation-based multiple shooting (DSMS) framework that transforms kinematically feasible references into dynamically feasible whole-body trajectories. By embedding a differentiable simulator within a nonlinear program, DSMS resolves contact, friction, impacts, self-collision, and joint limits internally while enforcing tracking, actuation, and task constraints without prescribing a contact schedule or introducing explicit contact constraints. Compared with existing retargeting methods, DSMS accelerates motion-imitation RL training and yields policies with high success rates and low tracking error. We further demonstrate zero-shot sim-to-real transfer on the Unitree G1 through command-conditioned contact-rich crawling and a highly dynamic 180-degree jump-turn.

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arXiv2026

Constrained Flow Matching via Lagrangian Dual Flows

Flow matching is a powerful tool for generative modeling, but emerging applications in robotics, planning, and physics require inference-time constraints on generated outputs. Such constraints are often complex and highly nonlinear. As a result, methods designed for linear constraints like image inpainting are rarely sufficient, and projection or optimization-based alternatives can be prohibitively expensive. In this paper, we introduce Lagrangian Dual Flows, a new family of constrained generation techniques based on Lagrangian dual dynamics. By simply flowing a dual co-state alongside generated samples, we can guarantee nonlinear constraint satisfaction without expensive optimization subproblems, pseudoinverses, or projection steps during the denoising process. The resulting constrained generation algorithms are simple, effective, and open new theoretical connections between flow matching and primal-dual methods in numerical optimization.

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arXiv2026

On Surprising Effects of Risk-Aware Domain Randomization for Contact-Rich Sampling-based Predictive Control

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

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arXiv2026

Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks

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.

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arXiv2025

CENIC: Convex Error-controlled Numerical Integration for Contact

State-of-the-art robotics simulators operate in discrete time. This requires users to choose a time step, which is both critical and challenging: large steps can produce non-physical artifacts, while small steps force the simulation to run slowly. Continuous-time error-controlled integration avoids such issues by automatically adjusting the time step to achieve a desired accuracy. But existing error-controlled integrators struggle with the stiff dynamics of contact, and cannot meet the speed and scalability requirements of modern robotics workflows. We introduce CENIC, a new continuous-time integrator that brings together recent advances in convex time-stepping and error-controlled integration, inheriting benefits from both continuous integration and discrete time-stepping. CENIC runs at fast real-time rates comparable to discrete-time robotics simulators like MuJoCo, Drake and Isaac Sim, while also providing guarantees on accuracy and convergence.

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arXiv2025

Equality Constrained Diffusion for Direct Trajectory Optimization

The recent success of diffusion-based generative models in image and natural language processing has ignited interest in diffusion-based trajectory optimization for nonlinear control systems. Existing methods cannot, however, handle the nonlinear equality constraints necessary for direct trajectory optimization. As a result, diffusion-based trajectory optimizers are currently limited to shooting methods, where the nonlinear dynamics are enforced by forward rollouts. This precludes many of the benefits enjoyed by direct methods, including flexible state constraints, reduced numerical sensitivity, and easy initial guess specification. In this paper, we present a method for diffusion-based optimization with equality constraints. This allows us to perform direct trajectory optimization, enforcing dynamic feasibility with constraints rather than rollouts. To the best of our knowledge, this is the first diffusion-based optimization algorithm that supports the general nonlinear equality constraints required for direct trajectory optimization.

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arXiv2025

Risk-Guided Diffusion: Toward Deploying Robot Foundation Models in Space, Where Failure Is Not An Option

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.

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arXiv2025

Inverse Dynamics Trajectory Optimization for Contact-Implicit Model Predictive Control

Robots must make and break contact with the environment to perform useful tasks, but planning and control through contact remains a formidable challenge. In this work, we achieve real-time contact-implicit model predictive control with a surprisingly simple method: inverse dynamics trajectory optimization. While trajectory optimization with inverse dynamics is not new, we introduce a series of incremental innovations that collectively enable fast model predictive control on a variety of challenging manipulation and locomotion tasks. We implement these innovations in an open-source solver and present simulation examples to support the effectiveness of the proposed approach. Additionally, we demonstrate contact-implicit model predictive control on hardware at over 100 Hz for a 20-degree-of-freedom bi-manual manipulation task. Video and code are available at https://idto.github.io.

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arXiv2025

DROP: Dexterous Reorientation via Online Planning

Achieving human-like dexterity is a longstanding challenge in robotics, in part due to the complexity of planning and control for contact-rich systems. In reinforcement learning (RL), one popular approach has been to use massively-parallelized, domain-randomized simulations to learn a policy offline over a vast array of contact conditions, allowing robust sim-to-real transfer. Inspired by recent advances in real-time parallel simulation, this work considers instead the viability of online planning methods for contact-rich manipulation by studying the well-known in-hand cube reorientation task. We propose a simple architecture that employs a sampling-based predictive controller and vision-based pose estimator to search for contact-rich control actions online. We conduct thorough experiments to assess the real-world performance of our method, architectural design choices, and key factors for robustness, demonstrating that our simple sampling-based approach achieves performance comparable to prior RL-based works. Supplemental material: https://caltech-amber.github.io/drop.

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arXiv2025

Reduced-Order Model Guided Contact-Implicit Model Predictive Control for Humanoid Locomotion

Humanoid robots have great potential for real-world applications due to their ability to operate in environments built for humans, but their deployment is hindered by the challenge of controlling their underlying high-dimensional nonlinear hybrid dynamics. While reduced-order models like the Hybrid Linear Inverted Pendulum (HLIP) are simple and computationally efficient, they lose whole-body expressiveness. Meanwhile, recent advances in Contact-Implicit Model Predictive Control (CI-MPC) enable robots to plan through multiple hybrid contact modes, but remain vulnerable to local minima and require significant tuning. We propose a control framework that combines the strengths of HLIP and CI-MPC. The reduced-order model generates a nominal gait, while CI-MPC manages the whole-body dynamics and modifies the contact schedule as needed. We demonstrate the effectiveness of this approach in simulation with a novel 24 degree-of-freedom humanoid robot: Achilles. Our proposed framework achieves rough terrain walking, disturbance recovery, robustness under model and state uncertainty, and allows the robot to interact with obstacles in the environment, all while running online in real-time at 50 Hz.

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arXiv2024

Supervised Learning for Stochastic Optimal Control

Supervised machine learning is powerful. In recent years, it has enabled massive breakthroughs in computer vision and natural language processing. But leveraging these advances for optimal control has proved difficult. Data is a key limiting factor. Without access to the optimal policy, value function, or demonstrations, how can we fit a policy? In this paper, we show how to automatically generate supervised learning data for a class of continuous-time nonlinear stochastic optimal control problems. In particular, applying the Feynman-Kac theorem to a linear reparameterization of the Hamilton-Jacobi-Bellman PDE allows us to sample the value function by simulating a stochastic process. Hardware accelerators like GPUs could rapidly generate a large amount of this training data. With this data in hand, stochastic optimal control becomes supervised learning.

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arXiv2023

Temporal Logic Motion Planning with Convex Optimization via Graphs of Convex Sets

Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics. In this paper, we cast Linear Temporal Logic (LTL) motion planning as a shortest path problem in a Graph of Convex Sets (GCS) and solve it with convex optimization. This approach brings together the best of modern optimization-based temporal logic planners and older automata-theoretic methods, addressing the limitations of each: we avoid clipping and passthrough by representing paths with continuous Bezier curves; computational complexity is polynomial (not exponential) in the number of sample points; global optimality can be certified (though it is not guaranteed); soundness and probabilistic completeness are guaranteed under mild assumptions; and most importantly, the method scales to complex specifications and high-dimensional systems, including a 30-DoF humanoid. Open-source code is available at https://github.com/vincekurtz/ltl_gcs.

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arXiv2022

Contact-Implicit Trajectory Optimization with Hydroelastic Contact and iLQR

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.

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arXiv2022

Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables

Signal Temporal Logic (STL) provides a convenient way of encoding complex control objectives for robotic and cyber-physical systems. The state-of-the-art in trajectory synthesis for STL is based on Mixed-Integer Convex Programming (MICP). The MICP approach is sound and complete, but has limited scalability due to exponential complexity in the number of binary variables. In this letter, we propose a more efficient MICP encoding for STL. Our new encoding is based on the insight that disjunction can be encoded using a logarithmic number of binary variables and conjunction can be encoded without binary variables. We demonstrate in simulation examples that our proposed approach significantly outperforms the state-of-the-art for long and complex specifications. Open-source software is available at https://stlpy.readthedocs.io.

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arXiv2022

Robust Approximate Simulation for Hierarchical Control of Piecewise Affine Systems under Bounded Disturbances

Piecewise affine (PWA) systems are widely applied in many practical cases such as the control of nonlinear systems and hybrid dynamics. However, most of the existing PWA control methods have poor scalability with respect to the number of modes and system dimensions and may not be robust to the disturbances in performance. In this paper, we present a robust approximate simulation based control method for PWA systems under bounded external disturbances. First, a lower-dimensional linear system (abstraction) and an associated interface are designed to enable the output of the PWA system (concrete system) to track the output of the abstraction. Then, a Lyapunov-like simulation function is designed to show the boundedness of the output errors between the two systems. Furthermore, the results obtained for linear abstraction are extended to the case that a simpler PWA system is the abstraction. To illustrate the effectiveness of the proposed approach, simulation results are provided for two design examples.

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arXiv2022

Mini Cheetah, the Falling Cat: A Case Study in Machine Learning and Trajectory Optimization for Robot Acrobatics

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.

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arXiv2021

A More Scalable Mixed-Integer Encoding for Metric Temporal Logic

The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is sound and complete, but struggles to scale to long and complex specifications. Drawing on recent advances in trajectory optimization for piecewise-affine systems, we propose a new MICP encoding for finite transition systems that significantly improves scalability to long and complex MTL specifications. Rather than seeking to reduce the number of variables in the MICP, we focus instead on designing an encoding with a tight convex relaxation. This leads to a larger optimization problem, but significantly improves branch-and-bound solver performance. In simulation experiments involving a mobile robot in a grid-world, the proposed encoding can reduce computation times by several orders of magnitude.

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arXiv2021

Active Perception and Control from PrSTL Specifications

Next-generation intelligent systems must plan and execute complex tasks with imperfect information about their environment. As a result, plans must also include actions to learn about the environment. This is known as active perception. Most active perception algorithms rely on reward or cost functions, which are usually challenging to specify and offer few theoretical guarantees. On the other hand, symbolic control methods can account for complex tasks using temporal logic but often do not deal well with uncertainties. This work combines symbolic control with active perception to achieve complex tasks in a partially observed and noisy control system with hybrid dynamics. Our basic idea is to employ a counterexample-guided-inductive-synthesis approach for control from probabilistic signal temporal logic (PrSTL) specifications. Our proposed algorithm combines bounded model checking (BMC) with sampling-based trajectory synthesis for uncertain hybrid systems. Active perception is inherently built into the framework because PrSTL formulas are defined in the chance domain.

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