Decomposition-Based Chance-Constrained Control for Timed Reach-Avoid Tasks

Abstract

This letter addresses the control problem of mobile robots with random noises under timed reach-avoid (TRA) tasks. TRA tasks are expressed as signal temporal logic (STL) formulas, and an optimization problem (OP) is formulated such that the chance constraint (CC) is embedded. To deal with the OP in the continuous-time setting, a local-to-global control strategy is proposed. We first decompose the STL formula into a finite number of local ones, and then decompose and convert the CC into deterministic constraints such that a finite number of local OPs are established and solved efficiently. The feasibility of all the local OPs implies the feasibility of the original OP, which results in a control strategy for the task accomplishment. The proposed strategy is further extended to the multi-robot case. Finally, numerical examples and comparisons are presented to illustrate the efficacy of the proposed control strategy.