Bezier Reachable Polytopes: Efficient Certificates for Robust Motion Planning with Layered Architectures

Control architectures are often implemented in a layered fashion, combining independently designed blocks to achieve complex tasks. Providing guarantees for such hierarchical frameworks requires considering the capabilities and limitations of each layer and their interconnections at design time. To address this holistic design challenge, we introduce the notion of Bezier Reachable Polytopes -- certificates of reachable points in the space of Bezier polynomial reference trajectories. This approach captures the set of trajectories that can be tracked by a low-level controller while satisfying state and input constraints, and leverages the geometric properties of Bezier polynomials to maintain an efficient polytopic representation. As a result, these certificates serve as a constructive tool for layered architectures, enabling long-horizon tasks to be reasoned about in a computationally tractable manner.

Dynamically Feasible Path Planning in Cluttered Environments via Reachable Bezier Polytopes

The deployment of robotic systems in real world environments requires the ability to quickly produce paths through cluttered, non-convex spaces. These planned trajectories must be both kinematically feasible (i.e., collision free) and dynamically feasible (i.e., satisfy the underlying system dynamics), necessitating a consideration of both the free space and the dynamics of the robot in the path planning phase. In this work, we explore the application of reachable Bezier polytopes as an efficient tool for generating trajectories satisfying both kinematic and dynamic requirements. Furthermore, we demonstrate that by offloading specific computation tasks to the GPU, such an algorithm can meet tight real time requirements. We propose a layered control architecture that efficiently produces collision free and dynamically feasible paths for nonlinear control systems, and demonstrate the framework on the tasks of 3D hopping in a cluttered environment.

Robust Adaptive Safe Robotic Grasping with Tactile Sensing

Robotic grasping requires safe force interaction to prevent a grasped object from being damaged or slipping out of the hand. In this vein, this paper proposes an integrated framework for grasping with formal safety guarantees based on Control Barrier Functions. We first design contact force and force closure constraints, which are enforced by a safety filter to accomplish safe grasping with finger force control. For sensory feedback, we develop a technique to estimate contact point, force, and torque from tactile sensors at each finger. We verify the framework with various safety filters in a numerical simulation under a two-finger grasping scenario. We then experimentally validate the framework by grasping multiple objects, including fragile lab glassware, in a real robotic setup, showing that safe grasping can be successfully achieved in the real world. We evaluate the performance of each safety filter in the context of safety violation and conservatism, and find that disturbance observer-based control barrier functions provide superior performance for safety guarantees with minimum conservatism. The demonstration video is available at https://youtu.be/Cuj47mkXRdg.

Get a Grip: Multi-Finger Grasp Evaluation at Scale Enables Robust Sim-to-Real Transfer

This work explores conditions under which multi-finger grasping algorithms can attain robust sim-to-real transfer. While numerous large datasets facilitate learning generative models for multi-finger grasping at scale, reliable real-world dexterous grasping remains challenging, with most methods degrading when deployed on hardware. An alternate strategy is to use discriminative grasp evaluation models for grasp selection and refinement, conditioned on real-world sensor measurements. This paradigm has produced state-of-the-art results for vision-based parallel-jaw grasping, but remains unproven in the multi-finger setting. In this work, we find that existing datasets and methods have been insufficient for training discriminitive models for multi-finger grasping. To train grasp evaluators at scale, datasets must provide on the order of millions of grasps, including both positive and negative examples, with corresponding visual data resembling measurements at inference time. To that end, we release a new, open-source dataset of 3.5M grasps on 4.3K objects annotated with RGB images, point clouds, and trained NeRFs. Leveraging this dataset, we train vision-based grasp evaluators that outperform both analytic and generative modeling-based baselines on extensive simulated and real-world trials across a diverse range of objects. We show via numerous ablations that the key factor for performance is indeed the evaluator, and that its quality degrades as the dataset shrinks, demonstrating the importance of our new dataset. Project website at: https://sites.google.com/view/get-a-grip-dataset.

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 sampled-based approach achieves performance comparable to prior RL-based works. Supplemental material: https://caltech-amber.github.io/drop.

Safety-critical Locomotion of Biped Robots in Infeasible Paths: Overcoming Obstacles during Navigation toward Destination

This paper proposes a safety-critical locomotion control framework employed for legged robots exploring through infeasible path in obstacle-rich environments. Our research focus is on achieving safe and robust locomotion where robots confront unavoidable obstacles en route to their designated destination. Through the utilization of outcomes from physical interactions with unknown objects, we establish a hierarchy among the safety-critical conditions avoiding the obstacles. This hierarchy enables the generation of a safe reference trajectory that adeptly mitigates conflicts among safety conditions and reduce the risk while controlling the robot toward its destination without additional motion planning methods. In addition, robust bipedal locomotion is achieved by utilizing the Hybrid Linear Inverted Pendulum model, coupled with a disturbance observer addressing a disturbance from the physical interaction.

Robust Agility via Learned Zero Dynamics Policies

We study the design of robust and agile controllers for hybrid underactuated systems. Our approach breaks down the task of creating a stabilizing controller into: 1) learning a mapping that is invariant under optimal control, and 2) driving the actuated coordinates to the output of that mapping. This approach, termed Zero Dynamics Policies, exploits the structure of underactuation by restricting the inputs of the target mapping to the subset of degrees of freedom that cannot be directly actuated, thereby achieving significant dimension reduction. Furthermore, we retain the stability and constraint satisfaction of optimal control while reducing the online computational overhead. We prove that controllers of this type stabilize hybrid underactuated systems and experimentally validate our approach on the 3D hopping platform, ARCHER. Over the course of 3000 hops the proposed framework demonstrates robust agility, maintaining stable hopping while rejecting disturbances on rough terrain.

Preferential Multi-Objective Bayesian Optimization

Preferential Bayesian optimization (PBO) is a framework for optimizing a decision-maker's latent preferences over available design choices. While preferences often involve multiple conflicting objectives, existing work in PBO assumes that preferences can be encoded by a single objective function. For example, in robotic assistive devices, technicians often attempt to maximize user comfort while simultaneously minimizing mechanical energy consumption for longer battery life. Similarly, in autonomous driving policy design, decision-makers wish to understand the trade-offs between multiple safety and performance attributes before committing to a policy. To address this gap, we propose the first framework for PBO with multiple objectives. Within this framework, we present dueling scalarized Thompson sampling (DSTS), a multi-objective generalization of the popular dueling Thompson algorithm, which may be of interest beyond the PBO setting. We evaluate DSTS across four synthetic test functions and two simulated exoskeleton personalization and driving policy design tasks, showing that it outperforms several benchmarks. Finally, we prove that DSTS is asymptotically consistent. As a direct consequence, this result provides, to our knowledge, the first convergence guarantee for dueling Thompson sampling in the PBO setting.

Dynamic Walking on Highly Underactuated Point Foot Humanoids: Closing the Loop between HZD and HLIP

Realizing bipedal locomotion on humanoid robots with point feet is especially challenging due to their highly underactuated nature, high degrees of freedom, and hybrid dynamics resulting from impacts. With the goal of addressing this challenging problem, this paper develops a control framework for realizing dynamic locomotion and implements it on a novel point foot humanoid: ADAM. To this end, we close the loop between Hybrid Zero Dynamics (HZD) and Hybrid linear inverted pendulum (HLIP) based step length regulation. To leverage the full-order hybrid dynamics of the robot, walking gaits are first generated offline by utilizing HZD. These trajectories are stabilized online through the use of a HLIP based regulator. Finally, the planned trajectories are mapped into the full-order system using a task space controller incorporating inverse kinematics. The proposed method is verified through numerical simulations and hardware experiments on the humanoid robot ADAM marking the first humanoid point foot walking. Moreover, we experimentally demonstrate the robustness of the realized walking via the ability to track a desired reference speed, robustness to pushes, and locomotion on uneven terrain.

Constructive Safety-Critical Control: Synthesizing Control Barrier Functions for Partially Feedback Linearizable Systems

Certifying the safety of nonlinear systems, through the lens of set invariance and control barrier functions (CBFs), offers a powerful method for controller synthesis, provided a CBF can be constructed. This paper draws connections between partial feedback linearization and CBF synthesis. We illustrate that when a control affine system is input-output linearizable with respect to a smooth output function, then, under mild regularity conditions, one may extend any safety constraint defined on the output to a CBF for the full-order dynamics. These more general results are specialized to robotic systems where the conditions required to synthesize CBFs simplify. The CBFs constructed from our approach are applied and verified in simulation and hardware experiments on a quadrotor.