Multi-robot coordination and safe learning using barrier certificates

The objective of this research is to develop a formal safety framework for collision-free and connectivity sustained motion in multi-robot coordination and learning based control. This safety framework is designed with barrier certificates, which provably guarantee the safety of dynamical systems based on the set invariance principle. The barrier certificates are enforced on the system using an online optimization-based controller such that minimal changes to the existing control strategies are required to guarantee safety. The proposed safety barrier certificates are validated on real multi-robot systems consisting of multiple Khepera robots, Magellan Pro robot, GRITS-Bots, and Crazyflie quadrotors.Ph.D

Safety Verification and Controller Synthesis for Systems with Input Constraints

In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our approach can be used to characterize the control invariance of a given set in terms of safety of a general nonlinear control system subject to input constraints. From the point of view of controller design, the proposed method provides an approach to synthesize a safe control law that guarantees that the trajectories of the system starting from a given initial set do not enter an unsafe set. Unlike the related control Barrier functions approach, our formulation only considers the vector field within the tangent cone of the zero level set defined by the certificates, and is shown to be less conservative by means of numerical evidence. For polynomial systems with semi-algebraic initial and safe sets, CBCs and safe control laws can be synthesized using sum-of-squares decomposition and semi-definite programming. Examples demonstrate our method

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems

Verification and Synthesis of Robust Control Barrier Functions: Multilevel Polynomial Optimization and Semidefinite Relaxation

We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust CBF verification and synthesis as multilevel polynomial optimization problems (POP), where verification optimizes -- in three levels -- the uncertainty, control, and state, while synthesis additionally optimizes the parameter of a chosen parametric CBF candidate. We then show that, by invoking the KKT conditions of the inner optimizations over uncertainty and control, the verification problem can be simplified as a single-level POP and the synthesis problem reduces to a min-max POP. This reduction leads to multilevel semidefinite relaxations. For the verification problem, we apply Lasserre's hierarchy of moment relaxations. For the synthesis problem, we draw connections to existing relaxation techniques for robust min-max POP, which first use sum-of-squares programming to find increasingly tight polynomial lower bounds to the unknown value function of the verification POP, and then call Lasserre's hierarchy again to maximize the lower bounds. Both semidefinite relaxations guarantee asymptotic global convergence to optimality. We provide an in-depth study of our framework on the controlled Van der Pol Oscillator, both with and without additive uncertainty.Comment: Accepted to IEEE Conference on Decision and Control (CDC) 202

A predictive safety filter for learning-based racing control

The growing need for high-performance controllers in safety-critical applications like autonomous driving has been motivating the development of formal safety verification techniques. In this paper, we design and implement a predictive safety filter that is able to maintain vehicle safety with respect to track boundaries when paired alongside any potentially unsafe control signal, such as those found in learning-based methods. A model predictive control (MPC) framework is used to create a minimally invasive algorithm that certifies whether a desired control input is safe and can be applied to the vehicle, or that provides an alternate input to keep the vehicle in bounds. To this end, we provide a principled procedure to compute a safe and invariant set for nonlinear dynamic bicycle models using efficient convex approximation techniques. To fully support an aggressive racing performance without conservative safety interventions, the safe set is extended in real-time through predictive control backup trajectories. Applications for assisted manual driving and deep imitation learning on a miniature remote-controlled vehicle demonstrate the safety filter's ability to ensure vehicle safety during aggressive maneuvers