为机械臂在不确定环境下生成安全轨迹，提供可证明的碰撞风险保障。
Provably Safe Trajectory Generation for Manipulators Under Motion and Environmental Uncertainties
- 用深度随机柯尔莫哥洛夫算子模型预测机械臂状态分布。
- 结合物理仿真与平方和优化，实现高效精确的碰撞风险验证。
- 适用于复杂场景下需要高安全性的机器人协同任务。
在不确定且非凸环境中的机器人机械臂运动规划面临巨大挑战，现有方法难以在复杂几何结构和非高斯不确定性下提供高效且形式化认证的碰撞风险保证。本文提出一种新型风险约束运动规划框架，融合刚性机械臂深度随机柯尔莫哥洛夫算子（RM-DeSKO）模型，以鲁棒预测机械臂在运动不确定性下的状态分布。进一步设计一种分层高效的验证方法，结合可并行的物理仿真与平方和（SOS）规划作为细粒度形式化认证的过滤器。该方法嵌入模型预测路径积分（MPPI）控制器中，首次利用SOS分解的二值碰撞信息改进策略。在两种典型机械臂上通过大量仿真与真实实验验证了该框架的有效性，包括具有挑战性的人机协作场景，展示了所学模型的仿真到现实迁移能力，以及在复杂、不确定环境下生成安全高效轨迹的能力。
原文摘要 · Abstract (English)
Robot manipulators operating in uncertain and non-convex environments present significant challenges for safe and optimal motion planning. Existing methods often struggle to provide efficient and formally certified collision risk guarantees, particularly when dealing with complex geometries and non-Gaussian uncertainties. This article proposes a novel risk-bounded motion planning framework to address this unmet need. Our approach integrates a rigid manipulator deep stochastic Koopman operator (RM-DeSKO) model to robustly predict the robot's state distribution under motion uncertainty. We then introduce an efficient, hierarchical verification method that combines parallelizable physics simulations with sum-of-squares (SOS) programming as a filter for fine-grained, formal certification of collision risk. This method is embedded within a Model Predictive Path Integral (MPPI) controller that uniquely utilizes binary collision information from SOS decomposition to improve its policy. The effectiveness of the proposed framework is validated on two typical robot manipulators through extensive simulations and real-world experiments, including a challenging human-robot collaboration scenario, demonstrating sim-to-real transfer of the learned model and its ability to generate safe and efficient trajectories in complex, uncertain settings.
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