Distributionally Robust Risk Map for Learning-Based Motion Planning and Control: A Semidefinite Programming Approach

In this article, we propose a novel safety specification tool, called the distributionally robust risk map (DR-risk map), for mobile robot operating in learning-enabled environment. Given robot's position, map aims to reliably assess conditional value-at-risk (CVaR) of collision with obstacles whose movements are inferred by Gaussian process regression (GPR). Unfortunately, distribution is subject errors, making it difficult accurately evaluate CVaR collision. To overcome challenge, our tool measures under worst-case so-called xmlns:xlink="http://www.w3.org/1999/xlink">ambiguity set that characterizes allowable errors. resolve infinite-dimensionality issue inherent construction DR-risk map, derive tractable semidefinite programming formulation provides an upper bound risk, exploiting techniques from modern distributionally optimization. As concrete application motion planning, RRT* algorithm considered using addresses errors caused GPR. Furthermore, control method devised learning-based model predictive (MPC) formulation. particular, neural network approximation proposed reduce computational cost solving MPC problem. The performance and utility demonstrated through simulation studies show its ability ensure robots despite learning