We present a motion planning algorithm for a class of uncertain control-affine nonlinear systems which guarantees runtime safety and goal reachability when using high-dimensional sensor measurements (e.g., RGB-D images) and a learned perception module in the feedback control loop. First, given a dataset of states and observations, we train a perception system that seeks to invert a subset of the state from an observation, and estimate an upper bound on the perception error which is valid with high probability in a trusted domain near the data. Next, we use contraction theory to design a stabilizing state feedback controller and a convergent dynamic state observer which uses the learned perception system to update its state estimate. We derive a bound on the trajectory tracking error when this controller is subjected to errors in the dynamics and incorrect state estimates. Finally, we integrate this bound into a sampling-based motion planner, guiding it to return trajectories that can be safely tracked at runtime using sensor data. We demonstrate our approach in simulation on a 4D car, a 6D planar quadrotor, and a 17D manipulation task with RGB(-D) sensor measurements, demonstrating that our method safely and reliably steers the system to the goal, while baselines that fail to consider the trusted domain or state estimation errors can be unsafe.

翻译：我们为一组不确定的控制-报复非线性系统提出了一个运动规划算法,该算法保证在使用高维传感器测量(例如 RGB-D 图像)和反馈控制环中学习的感知模块时,运行时间安全和目标可达性。首先,根据一组状态和观察数据,我们训练一个感知系统,试图从观察中倒转一个国家的子子子子,并估计在数据附近一个可信任域内高概率的感知错误的上限。接着,我们使用缩缩缩理论设计一个稳定状态反馈控制器和一个集中的动态国家观察员,该观察员利用所学的感知系统更新其状态估计。当该控制器在动态和不正确的状态估计中出现错误时,我们以轨迹追踪错误为约束。最后,我们将这一绑在基于抽样的运动规划器中,指导它返回在运行时可以安全跟踪到的轨迹。我们用4D 汽车、 6D 平面平面石器和17D 操纵任务,与RGB-D 传感器测量系统进行更新。 显示我们无法安全地测量,同时将测算出我们的域基线。