GP-GPIS-OPT: Grasp Planning Under Shape Uncertainty Using Gaussian Process Implicit Surfaces and Sequential Convex Programming

Computing grasps for an object is challenging when the object geometry is not known precisely; especially for objects that are difficult for robots to perceive, such as those with specular or transparent surfaces. These properties introduce uncertainty in object geometry, but commonly used polygonal mesh-based models cannot easily be extended to represent this uncertainty. In this paper, we explore the use of Gaussian process implicit surfaces (GPISs) to represent shape uncertainty directly from RGBD point cloud observations of objects. We study the use of GPIS representations to select grasps on previously unknown objects, measuring grasp quality by the probability of force closure. Our main contribution is GP-GPIS-OPT, an algorithm for computing grasps for paralleljaw grippers on 2D GPIS object representations. Specifically, we optimize an approximation to this quality subject to antipodal constraints on the parallel jaws using Sequential Convex Programming (SCP). We also introduce a method for visualizing 2D GPIS models based on blending shape samples from a GPIS. We test the algorithm on a set of perspective projections of objects that are difficult for robots to perceive. Our experiments suggest that GP-GPIS-OPT selects grasps with higher quality than a planner that ignores shape uncertainty on 7 of 8 of our test objects and is approximately 7.9× faster than the most common existing method for grasp planning under shape uncertainty. We also test our method with physical experiments on the Willow Garage PR2 robot.