用路径积分方法高效求解带时空逻辑约束的轨迹规划问题
Trajectory Planning with Signal Temporal Logic Costs using Deterministic Path Integral Optimization
- 基于模型预测路径积分控制，采样求解带信号时序逻辑代价的最优控制
- 在基准运动规划任务中实现高效求解，优于现有先进方法
- 适合需要精确时序约束的机器人轨迹规划场景
动态系统的期望行为建模常具挑战性。信号时序逻辑（STL）因其能形式化可理解、模块化且灵活的时空规范而被广泛采用。然而，随着规范复杂度增加及非光滑项出现，传统优化方法在处理STL相关问题时效率低下。平滑与近似技术虽可缓解此问题，但需改变原优化目标。本文提出一种基于模型预测路径积分控制的新颖采样方法，用于求解具有STL代价函数的最优控制问题。我们在基准运动规划问题上验证了该方法的有效性，并与当前最优方法进行了对比。结果表明，该方法能高效求解含STL代价的最优控制问题。
原文摘要 · Abstract (English)
Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal specifications. Due to scaling issues with respect to the complexity of the specifications and the potential occurrence of non-differentiable terms, classical optimization methods often solve STL-based problems inefficiently. Smoothing and approximation techniques can alleviate these issues but require changing the optimization problem. This paper proposes a novel sampling-based method based on model predictive path integral control to solve optimal control problems with STL cost functions. We demonstrate the effectiveness of our method on benchmark motion planning problems and compare its performance with state-of-the-art methods. The results show that our method efficiently solves optimal control problems with STL costs.
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