On the Construction of Safe Controllable Regions for Affine Systems with Applications to Robotics

TL;DR

This paper develops an efficient algorithm to construct in-block controllable regions for affine systems, facilitating safe control and collision avoidance in robotic applications including UAVs and ground robots.

Contribution

It introduces a novel computational method for constructing IBC regions, extending controllability analysis to practical region design for robotic systems.

Findings

The algorithm is computationally efficient and sound.

It successfully constructs safe speed profiles for various robots.

Experimental results demonstrate real-time collision avoidance for UAVs.

Abstract

This paper studies the problem of constructing in-block controllable (IBC) regions for affine systems. That is, we are concerned with constructing regions in the state space of affine systems such that all the states in the interior of the region are mutually accessible through the region's interior by applying uniformly bounded inputs. We first show that existing results for checking in-block controllability on given polytopic regions cannot be easily extended to address the question of constructing IBC regions. We then explore the geometry of the problem to provide a computationally efficient algorithm for constructing IBC regions. We also prove the soundness of the algorithm. We then use the proposed algorithm to construct safe speed profiles for different robotic systems, including fully-actuated robots, ground robots modeled as unicycles with acceleration limits, and unmanned aerial vehicles (UAVs). Finally, we present several experimental results on UAVs to verify the effectiveness of the proposed algorithm. For instance, we use the proposed algorithm for real-time collision avoidance for UAVs.