Provably Safe Trajectory Generation for Manipulators Under Motion and Environmental Uncertainties

2026-03-09

AI Summary

This work addresses the challenge of efficiently generating robot arm trajectories with formal safety guarantees in non-convex environments under motion and environmental uncertainties. The authors propose a risk-bounded motion planning framework that models non-Gaussian state distributions using a Rigid-body Moment-based Deep Stochastic Koopman Operator (RM-DeSKO), integrates Sum-of-Squares (SOS) programming for binary collision certification, and introduces a hierarchical parallel verification mechanism that fuses physics-based simulation with SOS analysis to enable fine-grained collision risk quantification. This certified safety assessment is then embedded into a Model Predictive Path Integral (MPPI) controller, achieving— for the first time—provably safe trajectory optimization and sim-to-real transfer under non-Gaussian uncertainty. Experiments on two robotic manipulators and human-robot collaboration scenarios demonstrate the method’s safety, computational efficiency, and generalization capability.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

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.

Problem

• trajectory generation
• motion planning
• collision risk
• uncertainty
• robot manipulators

Innovation

• RM-DeSKO
• risk-bounded motion planning
• sum-of-squares programming
• Model Predictive Path Integral
• formal safety verification