Distributionally robust risk map for learning-based motion planning and control: A semidefinite programming approach

by   Astghik Hakobyan, et al.

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


page 2

page 4

page 10

page 15

page 21

page 22

page 23

page 25


Learning-based distributionally robust motion control with Gaussian processes

Safety is a critical issue in learning-based robotic and autonomous syst...

Wasserstein Distributionally Robust Motion Control for Collision Avoidance Using Conditional Value-at-Risk

In this paper, a risk-aware motion control scheme is considered for mobi...

Risk-Averse Receding Horizon Motion Planning

This paper studies the problem of risk-averse receding horizon motion pl...

Risk-Sensitive Motion Planning using Entropic Value-at-Risk

We consider the problem of risk-sensitive motion planning in the presenc...

Risk-Aware Motion Planning in Partially Known Environments

Recent trends envisage robots being deployed in areas deemed dangerous t...

RAT iLQR: A Risk Auto-Tuning Controller to Optimally Account for Stochastic Model Mismatch

Successful robotic operation in stochastic environments relies on accura...

Risk-Aware Off-Road Navigation via a Learned Speed Distribution Map

Motion planning in off-road environments requires reasoning about both t...

Please sign up or login with your details

Forgot password? Click here to reset