This paper details a novel approach to collision avoidance for aerial vehicles that enables high-speed flight in uncertain environments. This framework is applied at the controller level and provides safety regardless of the planner that is used. The method is shown to be robust to state uncertainty and disturbances, and is computed entirely online utilizing the full nonlinear system dynamics. The effectiveness of this method is shown in a high-fidelity simulation of a quadrotor with onboard sensors rapidly and safely exploring a cave environment utilizing a simple planner.

In many multirobot applications, planning trajectories in a way to guarantee that the collective behavior of the robots satisfies a certain high-level specification is crucial. Motivated by this problem, we introduce counting temporal logics-formal languages that enable concise expression of multirobot task specifications over possibly infinite horizons in this article. We first introduce a general logic called counting linear temporal logic plus (cLTL+), and propose an optimization-based method that generates individual trajectories such that satisfaction of a given cLTL+ formula is guaranteed when these trajectories are synchronously executed. We then introduce a fragment of cLTL+, called counting linear temporal logic (cLTL), and show that a solution to a planning problem with cLTL constraints can be obtained more efficiently if all robots have identical dynamics. In the second part of this article, we relax the synchrony assumption and discuss how to generate trajectories that can be asynchronously executed, while preserving the satisfaction of the desired cLTL+ specification. In particular, we show that when the asynchrony between robots is bounded, the method presented in this article can be modified to generate robust trajectories. We demonstrate these ideas with an experiment and provide numerical results that showcase the scalability of the method.

Future manufacturing environments will see an increased need for cooperation between humans and machines. In this paper we propose a method that allows industrial manipulators to safely operate around humans. This approach guarantees that the manipulator will never collide with human operators while performing its normal tasks. This is done in an near-optimal way by considering how forward reachable sets of human operators grow with time, and by continuously updating these reachable sets based on current position estimates of the operators near the robot. An implicit active set invariance filter is then used to constrain the system-in a minimally invasive way-to stay in the complement of that forward reachable set. We demonstrate this approach in simulation on an industrial robotic arm: the ABB IRB 6640.

This paper employs correct-by-construction control synthesis, in particular controlled invariant set computations, for falsification. Our hypothesis is that if it is possible to compute a “large enough” controlled invariant set either for the actual system model or some simplification of the system model, interesting corner cases for other control designs can be generated by sampling initial conditions from the boundary of this controlled invariant set. Moreover, if falsifying trajectories for a given control design can be found through such sampling, then the controlled invariant set can be used as a supervisor to ensure safe operation of the control design under consideration. In addition to interesting initial conditions, which are mostly related to safety violations in transients, we use solutions from a dual game, a reachability game for the safety specification, to find falsifying inputs. We also propose optimization-based heuristics for input generation for cases when the state is outside the winning set of the dual game. To demonstrate the proposed ideas, we consider case studies from basic autonomous driving functionality, in particular, adaptive cruise control and lane keeping. We show how the proposed technique can be used to find interesting falsifying trajectories for classical control designs like proportional controllers, proportional integral controllers and model predictive controllers, as well as an open source real-world autonomous driving package.

Modern control synthesis methods that are capable of delivering safety guarantees typically rely on finding invariant sets. Computing and/or representing such sets becomes intractable for high-dimensional systems and often constitutes the main bottleneck of computational procedures. In this paper we instead analytically study a particular high-dimensional system and propose a control strategy that we prove renders a set invariant whenever it is possible to do so. The control problem---the mode-counting problem with two modes in one dimension---is inspired by scheduling of thermostatically controlled loads (TCLs) and exhibits a trade-off between local safety constraints and a global counting constraint. We improve upon a control strategy from the literature to handle heterogeneity and derive sufficient conditions for the strategy to solve the problem at hand. In addition, we show that the conditions are also necessary for the problem to have a solution, which implies a type of optimality of the proposed control strategy. We outline more general problem instances where the same control strategy can be implemented and we give sufficient (but not necessary) conditions for the closed-loop system to satisfy its specification. We illustrate our results on a TCL scheduling example.

Given a large homogeneous collection of switched systems, we consider a novel class of safety constraints, called mode-counting constraints, that impose restrictions on the number of systems that are in a particular mode. We propose an approach for synthesizing correct-by-construction switching protocols to enforce such constraints over time. Our approach starts by constructing an approximately bisimilar abstraction of the individual system model. Then, we show that the aggregate behavior of the collection can be represented by a linear system, whose system matrices are induced by the transition graph of the abstraction. Finally, the control synthesis problem with mode-counting constraints is reduced to a cycle assignment problem on the transition graph. One salient feature of the proposed approach is its scalability; the computational complexity is independent of the number of systems involved. We illustrate this approach on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time.