Control barrier functions (CBFs) have been recently considered for ensuring safety of nonlinear input-affine systems by means of appropriately designed controllers rendering a desired superlevel set of the CBF function forward invariant. In this work, we consider the safety control problem for nonlinear input-affine systems with multiple time-varying input delays. In order to ensure safety, we first design a set of predictors that estimate the state of the system at different future times by utilizing the control laws designed to ensure safety of the delay-free system. Under the assumption of perfect estimation of the future states, we show that under the designed controller, the closed-loop performance of the systems with and without the input delays is the same by the time the input with the largest delay acts on the system with delays for the first time.

In this work we pursue the problem of distributed distance-based formation control with prescribed transient and steady state behavior under connectivity and collision avoidance constraints. In addition to the distance-based formation a subset of agents is enforced to reach a desired distance from a dynamic virtual leader with bounded velocity under prescribed transient and steady state constraints while preserving connectivity with the virtual leader and a desired safety distance. We show that the aforementioned objectives can be ensured when the communication graph is an undirected tree and a single agent has access to the virtual leader's state information. Under these conditions we propose a model-free control law for known nonlinear systems as also an adaptive controller when the nonlinear dynamics of the agents are considered unknown and approximated using neural networks. Simulation results verify the effectiveness of the proposed controller both for known and unknown dynamics.

Coordination of multiple platoons involves the design of vehicles' trajectories ensuring splitting and merging of different platoons in a safe and energy-optimal manner. In this work, we consider the split-merge-maintain problem between any pair of platoons in which a number of vehicles temporally split from the rest, allowing the vehicles of another platoon to merge, and move with the preceding and following vehicles as a single, large platoon. Here, the splitting, merging and distance-maintaining tasks are expressed in Signal Temporal Logic (STL) and a control barrier function (CBF) is introduced to encode the STL constraints. The control inputs of the vehicles are, then, found as a solution to a computationally efficient, convex, quadratic program. The effectiveness of the proposed method is verified in simulation.

In this work we consider the control problem of systems that are subject to disjunctions of Signal Temporal Logic (STL) tasks. Motivated by existing approaches encoding the STL tasks utilizing time-varying control barrier functions (CBFs), we propose a continuously differentiable function for encoding the STL constraints that is defined as the composition of a smooth approximator of the max operator and a set of functions ensuring the satisfaction of the corresponding STL tasks with a desired robustness, and derive conditions for the choice of the class K function (when the latter is considered to be linear) to ensure that the proposed function is a CBF. Then, a control law ensuring the satisfaction of the STL task is found as a solution to a computationally efficient QP.

In this work we consider the problem of control under Signal Temporal Logic specifications (STL) that depend on relative position information among neighboring agents. In particular, we consider STL tasks for given pairs of agents whose satisfaction is translated into a set of setpoint output tracking problems with transient and steady-state constraints. Contrary to existing work the proposed framework does not require initial satisfaction of the funnel constraints but can ensure their satisfaction within a pre-specified finite time. Given a tree topology in which agents sharing a STL task form an edge, we show that the resulting control laws ensure the satisfaction of the STL task as well as boundedness of all closed loop signals using only local information.

In this work a continuous-time MPC scheme is presented for linear systems under Signal Temporal Logic (STL) specifications and input constraints. The satisfaction of the STL specifications is encoded by time-varying barrier functions and a least-violating control law is designed for cases when the satisfaction of the task with a given robustness value is not achieved, e.g., due to actuation limitations. The recursive feasibility of the proposed scheme is guaranteed when a time-varying terminal constraint is introduced. This constraint ensures a desired behavior for the system that guarantees the satisfaction of the task with pre-determined robustness.

Signal Temporal Logic (STL) has been found an expressive language for describing complex, time-constrained tasks in several robotic applications. Existing methods encode such specifications by either using integer constraints or by employing set invariance techniques. While in the first case this results in MILP control problems, in the latter case designer-specific choices may induce conservatism in the robot's performance and the satisfaction of the task. In this paper a continuous-time receding horizon control scheme (RHS) is proposed that exploits the trade-off between task satisfaction and performance costs such as actuation and state costs, traditionally considered in RHS schemes. The satisfaction of the STL tasks is encoded using time-varying control barrier functions (CBFs) that are designed online, thus avoiding the integer expressions that are often used in literature. The recursive feasibility of the proposed scheme is guaranteed by the satisfaction of a time-varying terminal constraint that ensures the satisfaction of the task with pre-determined robustness. The effectiveness of the method is illustrated in a multi-robot simulation scenario.

In this letter we focus on the problem of decomposing a global Signal Temporal Logic formula (STL) assigned to a multi-agent system to local STL tasks when the team of agents is a-priori decomposed to disjoint subteams. The predicate functions associated to the local tasks are parameterized as hypercubes depending on the states of the agents in a given sub-team. The parameters of the functions are, then, found as part of the solution of a convex program that aims implicitly at maximizing the volume of the zero superlevel set of the corresponding predicate function. Two alternative definitions of the local STL tasks are proposed and the satisfaction of the global STL formula is proven when the conjunction of the local STL tasks is satisfied.

In this letter a distributed model predictive control scheme (dMPC) is proposed for a multi-agent team that is subject to a set of time-constrained spatial tasks encoded in Signal Temporal Logic (STL). Here, the agents are subject to both individual and collaborative STL tasks. In order to ensure the satisfaction of the collaborative tasks while avoiding the computational burden of a centralized problem, we propose a sequential dMPC scheme and show the recursive feasibility property of the framework given appropriately designed terminal ingredients. The resulting MPC problems are solved in discrete-time yet continuous-time satisfaction of the STL tasks is ensured with appropriate tightening of the constraint sets.