4 research outputs found
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 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.Comment: 17 pages, 18 figures, under review for publication in Automatic
Inductive Certificate Synthesis for Control Design
The focus of this thesis is developing a framework for designing correct-by-construction controllers using control certificates. We use nonlinear dynamical systems to model the physical environment (plants). The goal is to synthesize controllers for these plants while guaranteeing formal correctness w.r.t. given specifications. We consider different fundamental specifications including stability, safety, and reach-while-stay. Stability specification states that the execution traces of the system remain close to an equilibrium state and approach it asymptotically. Safety specification requires the execution traces to stay in a safe region. Finally, for reach-while-stay specification, safety is needed until a target set is reached.The design task consists of two phases. In the first phase, the control design problem is reduced to the question of finding a control certificate. More precisely, the goal of the first phase is to define a class of control certificates with a specific structure. This definition should guarantee the following: ``Having a control certificate, one can systematically design a controller and prove its correctness at the same time."The goal in the second phase is to find such a control certificate. We define a potential control certificate space (hypothesis space) using parameterized functions. Next, we provide an inductive search framework to find proper parameters, which yield a control certificate. Finally, we evaluate our framework. We show that discovering control certificates is practically feasible and demonstrate the effectiveness of the automatically designed controllers through simulations and real physical systems experiments