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Register a new userBarrier Function-based Collaborative Control of Multiple Robots under Signal Temporal Logic Tasks
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Motivated by the recent interest in cyber-physical and autonomous robotic systems, we study the problem of dynamically coupled multi-agent systems under a set of signal temporal logic tasks. In particular, the satisfaction of each of these signal temporal logic tasks depends on the behavior of a distinct set of agents. Instead of abstracting the agent dynamics and the temporal logic tasks into a discrete domain and solving the problem therein or using optimization-based methods, we derive collaborative feedback control laws. These control laws are based on a decentralized control barrier function condition that results in discontinuous control laws, as opposed to a centralized condition resembling the single-agent case. The benefits of our approach are inherent robustness properties typically present in feedback control as well as satisfaction guarantees for continuous-time multi-agent systems. More specifically, time-varying control barrier functions are used that account for the semantics of the signal temporal logic tasks at hand. For a certain fragment of signal temporal logic tasks, we further propose a systematic way to construct such control barrier functions. Finally, we show the efficacy and robustness of our framework in an experiment including a group of three omnidirectional robots.
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We study the problem of controlling multi-agent systems under a set of signal temporal logic tasks. Signal temporal logic is a formalism that is used to express time and space constraints for dynamical systems. Recent methods to solve the control synthesis problem for single-agent systems under signal temporal logic tasks are, however, subject to a high computational complexity. Methods for multi-agent systems scale at least linearly with the number of agents and induce even higher computational burdens. We propose a computationally-efficient control strategy to solve the multi-agent control synthesis problem that results in a robust satisfaction of a set of signal temporal logic tasks. In particular, a decentralized feedback control law is proposed that is based on time-varying control barrier functions. The obtained control law is discontinuous and formal guarantees are provided by nonsmooth analysis. Simulations show the efficacy of the presented method.
The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose reactive risk signal interval temporal logic (ReRiSITL) as an extension of signal temporal logic (STL) to formulate complex spatiotemporal specifications. Unlike STL, ReRiSITL allows to consider uncontrollable propositions that may model humans as well as random environmental events such as sensor failures. Additionally, ReRiSITL allows to incorporate risk measures, such as (but not limited to) the Conditional Value-at-Risk, to measure the risk of violating certain spatial specifications. Second, we propose an algorithm to check if an ReRiSITL specification is satisfiable. For this purpose, we abstract the ReRiSITL specification into a timed signal transducer and devise a game-based approach. Third, we propose a reactive planning and control framework for dynamical control systems under ReRiSITL specifications.
A framework for the event-triggered control synthesis under signal temporal logic (STL) tasks is proposed. In our previous work, a continuous-time feedback control law was designed, using the prescribed performance control technique, to satisfy STL tasks. We replace this continuous-time feedback control law by an event-triggered controller. The event-triggering mechanism is based on a maximum triggering interval and on a norm bound on the difference between the value of the current state and the value of the state at the last triggering instance. Simulations of a multi-agent system quantitatively show the efficacy of using an event-triggered controller to reduce communication and computation efforts.
Temporal logics provide a formalism for expressing complex system specifications. A large body of literature has addressed the verification and the control synthesis problem for deterministic systems under such specifications. For stochastic systems or systems operating in unknown environments, however, only the probability of satisfying a specification has been considered so far, neglecting the risk of not satisfying the specification. Towards addressing this shortcoming, we consider, for the first time, risk metrics, such as (but not limited to) the Conditional Value-at-Risk, and propose risk signal temporal logic. Specifically, we compose risk metrics with stochastic predicates to consider the risk of violating certain spatial specifications. As a particular instance of such stochasticity, we consider control systems in unknown environments and present a determinization of the risk signal temporal logic specification to transform the stochastic control problem into a deterministic one. For unicycle-like dynamics, we then extend our previous work on deterministic time-varying control barrier functions.
Urban Air Mobility (UAM), or the scenario where multiple manned and Unmanned Aerial Vehicles (UAVs) carry out various tasks over urban airspaces, is a transportation concept of the future that is gaining prominence. UAM missions with complex spatial, temporal and reactive requirements can be succinctly represented using Signal Temporal Logic (STL), a behavioral specification language. However, planning and control of systems with STL specifications is computationally intensive, usually resulting in planning approaches that do not guarantee dynamical feasibility, or control approaches that cannot handle complex STL specifications. Here, we present an approach to co-design the planner and control such that a given STL specification (possibly over multiple UAVs) is satisfied with trajectories that are dynamically feasible and our controller can track them with a bounded tracking-error that the planner accounts for. The tracking controller is formulated for the non-linear dynamics of the individual UAVs, and the tracking error bound is computed for this controller when the trajectories satisfy some kinematic constraints. We also augment an existing multi-UAV STL-based trajectory generator in order to generate trajectories that satisfy such constraints. We show that this co-design allows for trajectories that satisfy a given STL specification, and are also dynamically feasible in the sense that they can be tracked with bounded error. The applicability of this approach is demonstrated through simulations of multi-UAV missions.
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