Safe Control Synthesis with Uncertain Dynamics and Constraints

TL;DR

This paper develops a unified approach for safe control synthesis under uncertain dynamics and constraints, using probabilistic and worst-case formulations that lead to efficient second-order cone programs, demonstrated through robot navigation simulations.

Contribution

It introduces novel probabilistic and robust CLF and CBF constraints that explicitly account for uncertainty, enabling efficient and safe control synthesis.

Findings

The approach results in SOCP formulations for both probabilistic and worst-case uncertainties.

Simulations show improved safety and stability over baseline methods.

The method effectively handles uncertainties in unknown environments.

Abstract

This paper considers safe control synthesis for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and the safety constraints. We formulate novel probabilistic and robust (worst-case) control Lyapunov function (CLF) and control barrier function (CBF) constraints that take into account the effect of uncertainty in either case. We show that either the probabilistic or the robust (worst-case) formulation leads to a second-order cone program (SOCP), which enables efficient safe and stable control synthesis. We evaluate our approach in PyBullet simulations of an autonomous robot navigating in unknown environments and compare the performance with a baseline CLF-CBF quadratic programming approach.