This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

Motivated by the recent interest in cyber-physical and interconnected autonomous systems, we study the problem of dynamically coupled multi-agent systems under conflicting local signal temporal logic (STL) tasks. Each agent is assigned a local STL task regardless of the tasks that the other agents are assigned to. Such a task may be dependent, i.e., the satisfaction of the task may depend on the behavior of more than one agent, so that the satisfaction of the conjunction of all local tasks may be conflicting. We propose a hybrid feedback control strategy using time-varying control barrier functions. Our control strategy finds least violating solutions in the aforementioned conflicting situations based on a suitable robustness notion and by initiating collaboration among agents.

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

Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert - a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization-based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.

Learning Control Barrier Functions from Expert Demonstrations

This article focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system are expressed as linear temporal logic specifications over finite traces. In particular, our approach decomposes the given specification into simpler reachability tasks based on its automata representation. We, then, propose the use of so-called control barrier certificate to solve those simpler reachability tasks along with computing the corresponding controllers and probability bounds. Finally, we combine those controllers to obtain a hybrid control policy solving the considered problem. Under some assumptions, we also provide two systematic approaches for uncountable and finite input sets to search for control barrier certificates. We demonstrate the effectiveness of the proposed approach on a room temperature control and lane keeping of a vehicle modeled as a four-dimensional single-track kinematic model. We compare our results with the discretization-based methods in the literature.

Formal Synthesis of Stochastic Systems via Control Barrier Certificates

Safe reinforcement learning: A control barrier function optimization approach

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.

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

Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance demands can be achieved for robotics applications. Prevailing use has assumed full knowledge of the safety barrier functions, however there are cases where the safe regions must be estimated online from sensor measurements. In these cases, the corresponding barrier function must be synthesized online. This paper describes a learning framework for estimating control barrier functions from sensor data. Doing so affords system operation in unknown state space regions without compromising safety. Here, a support vector machine classifier provides the barrier function specification as determined by sets of safe and unsafe states obtained from sensor measurements. Theoretical safety guarantees are provided. Experimental ROS-based simulation results for an omnidirectional robot equipped with LiDAR demonstrate safe operation.

Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach

In this article, we propose a framework for the control of mobile robots subject to temporal logic specifications using barrier functions. Complex task specifications can be conveniently encoded using linear temporal logic. In particular, we consider a fragment of linear temporal logic, which encompasses a large class of motion planning specifications for a robotic system. Control barrier functions have recently emerged as a convenient tool to guarantee reachability and safety for a system. In addition, they can be encoded as affine constraints in a quadratic program. In this article, a fully automatic framework that translates a user defined specification in temporal logic to a sequence of barrier function based quadratic programs is presented. In addition, with the aim of alleviating infeasibility scenarios, we propose methods for composition of barrier functions as well as a prioritization-based control method to guarantee feasibility of the controller. We prove that the resulting system trajectory synthesized by the proposed controller satisfies the given specification. Robotic simulation and experimental results are provided in addition to the theoretical framework.

Mohit Srinivasan

Papers

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

Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach

Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach

Control of Mobile Robots Using Barrier Functions Under Temporal Logic Specifications

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