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This paper tackles the challenge of motion planning for autonomous vehicles under conflicting Signal Temporal Logic (STL) specifications by formulating it as a lexicographic minimum-violation problem. They transform the multi-objective problem into a single-objective scalar optimization using non-uniform quantization and bit-shifting, enabling efficient solving with a deterministic Model Predictive Path Integral (MPPI) solver. The authors also introduce a novel predicate-robustness measure that combines spatial and temporal violations.
Prioritizing safety specs in robot motion planning doesn't have to be a computational nightmare: this work shows how to do it efficiently by cleverly reformulating the problem.
Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications. In situations where not all specifications can be met simultaneously, minimum-violation motion planning maintains system operation by minimizing violations of specifications in accordance with their priorities. Signal temporal logic (STL) provides a formal language for rigorously defining these specifications and enables the quantitative evaluation of their violations. However, a total ordering of specifications yields a lexicographic optimization problem, which is typically computationally expensive to solve using standard methods. We address this problem by transforming the multi-objective lexicographic optimization problem into a single-objective scalar optimization problem using non-uniform quantization and bit-shifting. Specifically, we extend a deterministic model predictive path integral (MPPI) solver to efficiently solve optimization problems without quadratic input cost. Additionally, a novel predicate-robustness measure that combines spatial and temporal violations is introduced. Our results show that the proposed method offers an interpretable and scalable solution for lexicographic STL minimum-violation motion planning within a single-objective solver framework.
