Safe navigation of cluttered environments is a critical challenge in robotics. It is typically approached by separating the planning and tracking problems, with planning executed on a reduced order model to generate reference trajectories, and control techniques used to track these trajectories on the full order dynamics. Inevitable tracking error necessitates robustification of the nominal plan to ensure safety; in many cases, this is accomplished via worst-case bounding, which ignores the fact that some trajectories of the planning model may be easier to track than others. In this work, we present a novel method leveraging massively parallel simulation to learn a dynamic tube representation, which characterizes tracking performance as a function of actions taken by the planning model. Planning model trajectories are then optimized such that the dynamic tube lies in the free space, allowing a balance between performance and safety to be traded off in real time. The resulting Dynamic Tube MPC is applied to the 3D hopping robot ARCHER, enabling agile and performant navigation of cluttered environments, and safe collision-free traversal of narrow corridors.

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 Bézier 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.

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.