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

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