Uncertainty is prevalent in robotics. Due to measurement noise and complex dynamics, we cannot estimate the exact system and environment state. Since conservative motion planners are not guaranteed to find a safe control strategy in a crowded, uncertain environment, we propose a density-based method. Our approach uses a neural network and the Liouville equation to learn the density evolution for a system with an uncertain initial state. We can plan for feasible and probably safe trajectories by applying a gradient-based optimization procedure to minimize the collision risk. We conduct motion planning experiments on simulated environments and environments generated from real-world data and outperform baseline methods such as model predictive control and nonlinear programming. While our method requires offline planning, the online run time is 100 times smaller compared to model predictive control.

翻译：摘要：不确定性在机器人领域普遍存在。由于测量噪声和复杂动力学，我们无法精确估计系统与环境状态。由于保守型运动规划器无法保证在拥挤的不确定环境中找到安全的控制策略，我们提出了一种基于密度的方法。该方法利用神经网络和Liouville方程学习具有不确定初始状态的系统的密度演化。通过应用基于梯度的优化过程来最小化碰撞风险，我们可以规划出可行且大概率安全的轨迹。我们在模拟环境和基于真实数据生成的环境中进行了运动规划实验，其性能优于模型预测控制和非线性规划等基线方法。尽管我们的方法需要离线规划，但其在线运行时间比模型预测控制小100倍。