Forward Invariance in Trajectory Spaces for Safety-critical Control

TL;DR

This paper introduces Forward Invariance in Trajectory Spaces (FITS), a novel safety-critical control framework that enhances safety adherence in robot control without compromising performance, by lifting safety constraints into trajectory space.

Contribution

FITS extends control barrier functions to trajectory spaces, enabling safe receding horizon control with provable safety guarantees and improved performance.

Findings

FITS outperforms traditional CBF and NMPC methods in safety adherence.

The quadratic program efficiently synthesizes safe trajectories.

Experiments demonstrate improved safety compliance without performance loss.

Abstract

Useful robot control algorithms should not only achieve performance objectives but also adhere to hard safety constraints. Control Barrier Functions (CBFs) have been developed to provably ensure system safety through forward invariance. However, they often unnecessarily sacrifice performance for safety since they are purely reactive. Receding horizon control (RHC), on the other hand, consider planned trajectories to account for the future evolution of a system. This work provides a new perspective on safety-critical control by introducing Forward Invariance in Trajectory Spaces (FITS). We lift the problem of safe RHC into the trajectory space and describe the evolution of planned trajectories as a controlled dynamical system. Safety constraints defined over states can be converted into sets in the trajectory space which we render forward invariant via a CBF framework. We derive an efficient quadratic program (QP) to synthesize trajectories that provably satisfy safety constraints. Our experiments support that FITS improves the adherence to safety specifications without sacrificing performance over alternative CBF and NMPC methods.