Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics. In this paper, we cast Linear Temporal Logic (LTL) motion planning as a shortest path problem in a Graph of Convex Sets (GCS) and solve it with convex optimization. This approach brings together the best of modern optimization-based temporal logic planners and older automata-theoretic methods, addressing the limitations of each: paths are represented with continuous Bezier curves, avoiding clipping and pass-through; computational complexity is polynomial (not exponential) in the number of sample points; global optimality can be certified; soundness and completeness are guaranteed under mild assumptions; and most importantly, the method scales to complex specifications and high-dimensional systems, including a 30-DoF humanoid. Open-source code is available at https://github.com/vincekurtz/ltl_gcs.

中文翻译：

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通过凸集图进行凸优化的时间逻辑运动规划

时间逻辑是指定复杂任务的简洁方法。但是实现时序逻辑规范的运动规划很困难，现有方法难以扩展到复杂规范和高维系统动力学。在本文中，我们将线性时间逻辑 (LTL) 运动规划作为凸集图 (GCS) 中的最短路径问题，并使用凸优化对其进行求解。这种方法汇集了现代基于优化的时序逻辑规划器和旧的自动机理论方法的精华，解决了每种方法的局限性：路径用连续的贝塞尔曲线表示，避免剪裁和传递；计算复杂度是样本点数量的多项式（非指数）；可以证明全局最优性；在温和的假设下保证稳健性和完整性；最重要的是，该方法可扩展到复杂规格和高维系统，包括 30-DoF 人形机器人。开源代码可在 https://github.com/vincekurtz/ltl_gcs 获得。