Geometry-Aware Safety-Critical Local Reactive Controller for Robot Navigation in Unknown and Cluttered Environments

TL;DR

This paper introduces a geometry-aware, safety-critical local reactive controller for robot navigation in unknown, cluttered environments, utilizing polynomial optimization and SOS techniques for real-time safety and trajectory tracking.

Contribution

It develops a novel polynomial optimization framework with SOS constraints that incorporate robot geometry, enabling real-time, safety-critical navigation in complex environments.

Findings

Effective in unknown cluttered environments

Ensures safety via polynomial positivity certificates

Achieves real-time performance with SDP convexification

Abstract

This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization problem. Then, safety constraints are imposed on the control variables invoking the notion of polynomial positivity certificates in conjunction with their Sum-of-Squares (SOS) approximation, thereby confining the robot motion inside the locally extracted convex free region. It is noteworthy that, in the process of devising the proposed safety constraints, the geometry of the robot can be approximated using any shape that can be characterized with a set of polynomial functions. The optimization problem is further convexified into a semidefinite program (SDP) leveraging truncated multi-sequences (tms) and moment relaxation, which favorably facilitates the effective use of off-the-shelf conic programming solvers, such that real-time performance is attainable. Various robot navigation tasks are investigated to demonstrate the effectiveness of the proposed approach in terms of safety and tracking performance.