Control of Multi-Agent Systems with Finite Time Control Barrier Certificates and Temporal Logic

Abstract

In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.

Decentralized Control Barrier Functions for Coupled Multi-Agent Systems under Signal Temporal Logic Tasks

“…Control barrier functions have first been proposed in [12] and guarantee the existence of a control law that renders a desired set forward invariant; [13] presents control barrier functions tailord for the safe robot navigation, while [14] presents decentralized control barrier functions for safe multi-robot navigation. Nonsmooth and time-varying control barrier functions have been proposed in [15] and [16], respectively; [17] uses finite time control barrier functions for single-agent systems under linear temporal logic tasks, hence not allowing explicit timing constraints.…”

Formation Control and Distributed Goal Assignment for Multi-Agent Non-Holonomic Systems

“…Transforming (18) using (16) and taking into account Assumption 2 (when the robot gets into the collision avoidance region, in the collision avoidance state, velocities v l and ω l are replaced with 0 value) error dynamics can be expressed in the following form: e ix = k 3 e iy e iθ − k 1 E iẋ e iy = −k 3 e iθ e iẋ e iθ = −k 3 e iθ .…”

“…Taking the first equation in (19), one can state that if ∂V aij ∂e ix is sufficiently high (that happens if the robot is very close to the obstacle; there is no problem of boundedness in the other cases (refer to the properties of the APF, Figure 1) ∂e iyė iy is less than zero the second term on the right hand side must be less than the first one taking their absolute values. This can be obtained by reducing k 3 parameter (refer to Equation (16)). The propertyV aij ≤ 0 guarantees boundedness of both V aij and ∂V aij ∂e ix .…”

“…In the method proposed in [15] control barrier functions are unified with performance objectives expressed as control Lyapunov functions. The authors of the paper [16] provide a theoretical framework to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent systems.…”

Control Barrier Functions for Multi-Agent Systems Under Conflicting Local Signal Temporal Logic Tasks

“…Nonsmooth and time-varying control barrier functions have appeared in [18] and [19], while robustness and input-to-state safety notions have been proposed in [20] and [21]. Barrier functions have also been used to control systems under temporal logic tasks; [13] establishes a connection between the semantics of an STL task and time-varying control barrier functions, while [22] considers finite time control barrier functions for LTL.…”