Provably Safe Trajectory Generation for Manipulators Under Motion and Environmental Uncertainties

TL;DR

This paper introduces a risk-bounded motion planning framework for robot manipulators operating in uncertain, complex environments, combining stochastic modeling, hierarchical verification, and MPC to ensure safety and efficiency.

Contribution

It presents a novel integration of a stochastic Koopman model, SOS-based formal verification, and MPC for safe trajectory generation under uncertainties in complex environments.

Findings

Effective collision risk certification in non-convex settings

Successful sim-to-real transfer in human-robot collaboration

Generation of safe, efficient trajectories in uncertain scenarios

Abstract

Robot manipulators operating in uncertain and non-convex environments present significant challenges for safe and optimal motion planning. Existing methods often struggle to provide efficient and formally certified collision risk guarantees, particularly when dealing with complex geometries and non-Gaussian uncertainties. This article proposes a novel risk-bounded motion planning framework to address this unmet need. Our approach integrates a rigid manipulator deep stochastic Koopman operator (RM-DeSKO) model to robustly predict the robot's state distribution under motion uncertainty. We then introduce an efficient, hierarchical verification method that combines parallelizable physics simulations with sum-of-squares (SOS) programming as a filter for fine-grained, formal certification of collision risk. This method is embedded within a Model Predictive Path Integral (MPPI) controller that uniquely utilizes binary collision information from SOS decomposition to improve its policy. The effectiveness of the proposed framework is validated on two typical robot manipulators through extensive simulations and real-world experiments, including a challenging human-robot collaboration scenario, demonstrating sim-to-real transfer of the learned model and its ability to generate safe and efficient trajectories in complex, uncertain settings.