Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems
Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems
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DOI：
10.1109/cdc45484.2021.9683354
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Glen Chou;N. Ozay;D. Berenson
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文献类型：
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作者：
Glen Chou;N. Ozay;D. Berenson
我们提出了一种基于收缩的反馈运动规划的局部增量指数稳定系统的未知动态，提供概率安全性和可达性保证的方法。给定一个动态数据集，我们的方法学习动态的深度控制仿射近似。为了找到一个可信的域，这个模型可以用于规划，我们获得了一个估计的Lipschitz常数的模型误差，这是有效的与给定的概率，在一个区域周围的训练数据，提供了一个本地的，空间变化的模型误差界。我们推导出一个轨迹跟踪误差界的收缩为基础的控制器，受到这个模型误差，然后学习控制器，优化这个跟踪界。在给定的概率下，验证了控制器的正确性和可信域中跟踪误差界的正确性。然后，我们使用与可信域绑定在一起的轨迹误差来指导基于采样的规划器返回可以在执行中鲁棒跟踪的轨迹。我们展示了4D汽车，6D四旋翼和22D可变形物体操作任务的结果，显示我们的方法使用高维欠驱动系统的学习模型安全地计划，而不考虑跟踪误差范围或可信域的基线计划可能无法稳定系统并变得不安全。
We present a method for contraction-based feed-back motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset, our method learns a deep control-affine approximation of the dynamics. To find a trusted domain where this model can be used for planning, we obtain an estimate of the Lipschitz constant of the model error, which is valid with a given probability, in a region around the training data, providing a local, spatially-varying model error bound. We derive a trajectory tracking error bound for a contraction-based controller that is subjected to this model error, and then learn a controller that optimizes this tracking bound. With a given probability, we verify the correctness of the controller and tracking error bound in the trusted domain. We then use the trajectory error bound together with the trusted domain to guide a sampling-based planner to return trajectories that can be robustly tracked in execution. We show results on a 4D car, a 6D quadrotor, and a 22D deformable object manipulation task, showing our method plans safely with learned models of high-dimensional underactuated systems, while baselines that plan without considering the tracking error bound or the trusted domain can fail to stabilize the system and become unsafe.