Safe Navigation of Bipedal Robots via Koopman Operator-Based Model Predictive Control

TL;DR

It is demonstrated that the Koopman-based model more accurately predicts bipedal robot trajectories than baseline approaches, and the proposed navigation framework achieves improved safety with better success rates in dense environments with narrow passages.

Abstract

Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under simple velocity commands, as their actual dynamics are governed by complex whole-body movements and discrete contacts. In this work, we propose a novel safe navigation framework inspired by Koopman operator theory. We first train a low-level locomotion policy using deep reinforcement learning, and then capture its low-frequency, base-level dynamics by learning linearized dynamics in a high-dimensional lifted space using Dynamic Mode Decomposition. Then, our model-predictive controller (MPC) efficiently optimizes control signals via standard quadratic objective and the linear dynamics constraint in the lifted space. We demonstrate that the Koopman-based model more accurately predicts bipedal robot trajectories than baseline approaches. Furthermore, we show that the proposed navigation framework achieves improved safety with better success rates in dense environments with narrow passages.

Figures (8)

• Figure 1: Our approach first trains a locomotion controller on a bipedal robot and then learns the linearized high-level dynamics using Koopman operator theory. Once the dynamics are learned, we use it to develop an MPC-style safe navigation controller.
• Figure 2: Our approach enables safe navigation in challenging environments with dense obstacles and narrow passages.
• Figure 3: Overview of the navigation framework.
• Figure 4: Long-term prediction error across the entire validation set. The bold line indicates the mean, and the shaded region shows the standard deviation.
• Figure 5: Comparison of a long-term prediction of Koopman model against the baselines ($\Delta t = 0.5$). The ground-truth trajectory is generated from a constant command not included in the training dataset. Koopman Forward Dynamics achieve two to four times less final step error compared to Linear and MLP baselines.