Cost-to-Go Function Generating Networks for High Dimensional Motion Planning

This paper presents c2g-HOF networks which learn to generate cost-to-go\nfunctions for manipulator motion planning. The c2g-HOF architecture consists of\na cost-to-go function over the configuration space represented as a neural\nnetwork (c2g-network) as well as a Higher Order Function (HOF) network which\noutputs the weights of the c2g-network for a given input workspace. Both\nnetworks are trained end-to-end in a supervised fashion using costs computed\nfrom traditional motion planners. Once trained, c2g-HOF can generate a smooth\nand continuous cost-to-go function directly from workspace sensor inputs\n(represented as a point cloud in 3D or an image in 2D). At inference time, the\nweights of the c2g-network are computed very efficiently and near-optimal\ntrajectories are generated by simply following the gradient of the cost-to-go\nfunction. We compare c2g-HOF with traditional planning algorithms for various\nrobots and planning scenarios. The experimental results indicate that planning\nwith c2g-HOF is significantly faster than other motion planning algorithms,\nresulting in orders of magnitude improvement when including collision checking.\nFurthermore, despite being trained from sparsely sampled trajectories in\nconfiguration space, c2g-HOF generalizes to generate smoother, and often lower\ncost, trajectories. We demonstrate cost-to-go based planning on a 7 DoF\nmanipulator arm where motion planning in a complex workspace requires only 0.13\nseconds for the entire trajectory.\n