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Robust Motion Planning in Dynamic Environments Based on Sampled-Data Hamilton–Jacobi Reachability

Published online by Cambridge University Press:  14 February 2020

Sébastien Kleff Open the ORCID record for Sébastien Kleff [Opens in a new window]  and
Ning Li
Sébastien Kleff
Affiliation:
Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail: sebastien.kleff@eleves.ec-nantes.fr Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, 200240, China
Ning Li*
Affiliation:
Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail: sebastien.kleff@eleves.ec-nantes.fr Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, 200240, China
*
*Corresponding author. E-mail: ning_li@sjtu.edu.cn
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Summary

We propose a novel formal approach to robust motion planning (MP) in dynamic environments based on reachability analysis. While traditional MP methods usually fail to provide formal robust safety and performance guarantees, our approach provably ensures safe task achievement in time-varying and adversarial environments under parametric uncertainty. We leverage recent results on Hamilton–Jacobi (HJ) reachability and differential games in order to compute offline guaranteed motion plans that are compatible with the sampled-data (SD) paradigm. Also, we synthesize online provably robust safety-preserving and target-reaching feedback controls. Unlike earlier applications of reachability analysis to MP, our methodology handles arbitrary time-varying constraints, adversarial agents such as pursuing obstacles or evading targets, and takes into account the robot’s configuration. Furthermore, we use HJ projections in order to reduce significantly the computational burden without trading off safety guarantees. The validity of this approach is demonstrated through the case study of a robot arm subject to measurement errors, which is tasked with safely reaching a goal in a known time-varying workspace while avoiding capture by an unpredictable pursuer. Finally, the performance of the approach and research perspectives are discussed.

Keywords

Robust motion planningReachability analysisSampled-data systemReach-avoid gameHamilton–Jacobi–Isaacs Equation
Type
Articles
Information
Robotica , Volume 38 , Issue 12 , December 2020 , pp. 2151 - 2172
Copyright
Copyright © Cambridge University Press 2020

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