Robots are used increasingly often in safety-critical scenarios, such as robotic surgery or human–robot interaction. To ensure stringent performance criteria, formal controller synthesis is a promising direction to guarantee that robots behave as desired. However, formally ensured properties only transfer to the real robot when the model is appropriate. In this article, we address this problem by combining the identification of a reachset-conformant model with controller synthesis. Since the reachset-conformant model contains all the measured behaviors of the real robot, the safety properties of the model transfer to the real robot. The transferability is demonstrated by experiments on a real robot, for which we synthesize tracking controllers.

We present a MATLAB toolbox for Automated Reachset Optimal Control (AROC) that automatically synthesizes verified controllers for solving reach-avoid problems using reachability analysis. The toolbox implements two different types of control approaches: When using our verified model predictive controller, a feasible control law is constructed and verified on-the-fly during online application of the system. For motion-primitive-based control, on the other hand, controllers for many motion primitives are synthesized offline and then used for online motion planning with a maneuver automaton. Since our toolbox considers general nonlinear systems with input constraints, state constraints, and bounded disturbances, it is applicable to a very broad class of systems, as we demonstrate with several numerical examples. AROC is available at https://aroc.in.tum.de.

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few. In many of these applications, one requires to compute a reachable set starting within a previously computed reachable set. While it was previously required to re-compute the entire reachable set, we demonstrate that one can leverage the dependencies of states within the previously computed set. As a result, we almost instantly obtain an over-approximative subset of a previously computed reachable set by evaluating analytical maps. The advantages of our novel method are demonstrated for falsification of systems, optimization over reachable sets, and synthesizing safe maneuver automata. In all of these applications, the computation time is reduced significantly.

A new control method for nonlinear systems is presented which solves reach-avoid problems by interpolating optimal solutions using convex combinations. It also provides formal guarantees for constraint satisfaction and safety. Reach-avoid problems are important control tasks, which arise in many modern cyber-physical systems, including autonomous driving and robotic path planning. We obtain our control policy by computing the optimal input trajectories for finitely many extreme states only and combining them using convex combinations for all states in a continuous set. Our approach has very low online computation complexity, making it applicable for fast dynamical systems. Iterating through our approach leads to a new form of feedback control with formal guarantees in the presence of disturbances. We demonstrate the new control method for a control problem in automated driving and show the advantages compared to a classical control method.

Bipedal robots are prime examples of complex cyber-physical systems (CPS). They exhibit many of the features that make the design and verification of CPS so difficult: hybrid dynamics, large continuous dynamics in each mode (e.g., 10 or more state variables), and nontrivial specifications involving nonlinear constraints on the state variables. In this paper, we propose a two-step approach to formally synthesize control software for bipedal robots so as to enforce specifications by design and thereby generate physically realizable stable walking. In the first step, we design outputs and classical controllers driving these outputs to zero. The resulting controlled system evolves on a lower dimensional manifold and is described by the hybrid zero dynamics governing the remaining degrees of freedom. In the second step, we construct an abstraction of the hybrid zero dynamics that is used to synthesize a controller enforcing the desired specifications to be satisfied on the full order model. Our two step approach is a systematic way to mitigate the curse of dimensionality that hampers the applicability of formal synthesis techniques to complex CPS. Our results are illustrated with simulations showing how the synthesized controller enforces all the desired specifications and offers improved performance with respect to a controller that was utilized to obtain walking experimentally on the bipedal robot AMBER 2.