On the construction of safe controllable regions for affine systems with applications to robotics

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 within 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 robotic systems. As a case study, we present several experimental results on unmanned aerial vehicles (UAVs) to verify the effectiveness of the proposed algorithm; these results include using the proposed algorithm for real-time collision avoidance for UAVs.