Distance metric approximation for state-space RRTs using supervised learning

The dynamic feasibility of solutions to motion planning problems using Rapidly Exploring Random Trees depends strongly on the choice of the distance metric used while planning. The ideal distance metric is the optimal cost of traversal between two states in the state space. However, it is computationally intensive to find the optimal cost while planning. We propose a novel approach to overcome this barrier by using a supervised learning algorithm that learns a nonlinear function which is an estimate of the optimal cost, via offline training. We use the Iterative Linear Quadratic Regulator approach for estimating an approximation to the optimal cost and learn this cost using Locally Weighted Projection Regression. We show that the learnt function approximates the original cost with a reasonable tolerance and more importantly, gives a tremendous speed up of a factor of 1000 over the actual computation time. We also use the learnt metric for solving the pendulum swing up planning problem and show that our metric performs better than the popularly used Linear Quadratic Regulator based metric.