Stochastic Modeling of Distance to Collision for Robot Manipulators

Evaluating distance to collision for robot manipulators is useful for assessing the feasibility of a robot configuration or for defining safe robot motion in unpredictable environments. However, distance estimation is a time-consuming operation, and the sensors involved in measuring the distance are always noisy. A challenge thus exists in evaluating the expected distance to collision for safer robot control and planning. In this work, we propose the use of Gaussian process (GP) regression and the forward kinematics (FK) kernel (a similarity function for robot manipulators) to efficiently and accurately estimate distance to collision. We show that the GP model with the FK kernel achieves almost 70 times faster distance evaluations compared to a standard geometric technique, and up to 18 times more accurate evaluations compared to other regression models, even when the GP is trained on noisy distance measurements. We employ this technique in trajectory optimization tasks and observe 13 times faster optimization than with the noise-free geometric approach yet obtain similar optimized motion plans. We also propose a confidence-based hybrid model that uses model-based predictions in regions of high confidence and switches to a more expensive sensor-based approach in other areas, and we demonstrate the usefulness of this hybrid model in an application involving reaching into a narrow passage.