Robots with the ability to balance time against the thoroughness of search have the potential to provide time-critical assistance in applications such as search and rescue. Current advances in ergodic coverage-based search methods have enabled robots to completely explore and search an area in a fixed amount of time. However, optimizing time against the quality of autonomous ergodic search has yet to be demonstrated. In this paper, we investigate solutions to the time-optimal ergodic search problem for fast and adaptive robotic search and exploration. We pose the problem as a minimum time problem with an ergodic inequality constraint whose upper bound regulates and balances the granularity of search against time. Solutions to the problem are presented analytically using Pontryagin's conditions of optimality and demonstrated numerically through a direct transcription optimization approach. We show the efficacy of the approach in generating time-optimal ergodic search trajectories in simulation and with drone experiments in a cluttered environment. Obstacle avoidance is shown to be readily integrated into our formulation, and we perform ablation studies that investigate parameter dependence on optimized time and trajectory sensitivity for search.

翻译：具备平衡搜索时间与搜索彻底性能力的机器人，可在搜救等应用中提供时间关键性辅助。当前遍历覆盖搜索方法的进展使机器人能够在固定时间内完全探索并搜索区域，但如何优化搜索时间与自主遍历搜索质量之间的平衡尚未得到验证。本文针对快速自适应机器人搜索与探索问题，研究时间最优遍历搜索的求解方案。我们将该问题建模为带有遍历不等式约束的最小时间问题，其上限约束可调节并平衡搜索粒度与时间成本。利用庞特里亚金最优性条件解析推导该问题的解，并通过直接转录优化方法进行数值验证。我们在仿真环境及杂乱环境中的无人机实验中展示了该方法生成时间最优遍历搜索轨迹的有效性。障碍物规避可便捷地集成至本框架中，并开展消融实验以探究参数对优化时间的影响及轨迹搜索敏感性。