Dynamic Tube MPC: Learning Tube Dynamics with Massively Parallel Simulation for Robust Safety in Practice

TL;DR

A novel method leveraging massively parallel simulation to learn a dynamic tube representation is presented, which characterizes tracking performance as a function of actions taken by the planning model, and is applied to the 3D hopping robot ARCHER, enabling agile and performant navigation of cluttered environments, and safe collision-free traversal of narrow corridors.

Abstract

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.

Figures (4)

• Figure 2: ARCHER plans a collision-free path through a cluttered environment by jointly optimizing a path on a reduced order model and a dynamic tube, whose dynamics are learned from simulation data. The obstacles are tightly approximated by circles and buffered by the radius of the robot.
• Figure 3: Analysis of the impact of history, $H$, on tube prediction accuracy; tube dynamics are trained on the hopper dynamics for several values of $H$. (Left) Evaluation on a 20% holdout from training data, Mean Error when Correct is plotted against history length. (Middle) a portion of a square trajectory is executed in IsaacGym on ARCHER. (Right) The error signal, $e_k$, is plotted in black, with the tube predictions, $w_k$, plotted at three points in time, $k=25,75, 145$ over a horizon of $N=50$ nodes (right pane). We see short horizon models being both overly conservative and violating the error tube.
• Figure 4: Three Tube MPC variants, on a problem where the hopper must traverse a narrow gap. (Top) Tube MPC, where the tube size is fixed to be the 90% quantile in a dataset collected with $\bar{v}=0.2$m/s. (Middle) Tube MPC, where the tube size is fixed to the 90% quantile, in a dataset collected with $\bar{v}=0.04$m/s. (Bottom) Dynamic Tube MPC using recursive tube dynamics, which simultaneously achieves performance and safety.
• Figure 5: Implementation of Dynamic Tube MPC on the ARCHER platform. Plotted are closed loop planned trajectory and tube (white), along with tracking performance (red), along with tube, state, and input trajectories over time. Note specifically how the planning model slows down when in narrow corridors between obstacles to improve tracking.