Safe Control of Multiagent Systems via Low-Complexity Control Barrier Functions

In its standard formulation, the Control Barrier Function (CBF) method scales poorly as the order of the system dynamics increases. On the one hand, the need of recursively extending the control with higher-order terms along the backstepping procedure inevitably results in dynamically increasing complexity. On the other hand, the lack of an explicit form of the CBF leads to implicit formulations of the safety conditions, to be solved numerically via quadratic programming. These high complexity and poor scalability issues further amplify in multi-agent systems. This work proposes a low-complexity framework for safe control of higher-order multi-agent systems within the philosophy of funnel control. Different from the state of the art, safety is expressed in terms of a CBF that is explicitly constructed from funnel functions, thus providing a solution to the well-known problem of lack of systematic methods for constructing a CBF. Low complexity comes from the fact that the control does not involve complex dynamical extensions during the backstepping procedure. Notably, the proposed CBF is shown to automatically satisfy by design the safety conditions, without resorting to any quadratic programming. Lyapunov analysis shows that the design allows to consider individual terms for stability and safety, so as to accomplish these tasks in a seamless integrated fashion. Simulation studies and comparisons with the state of the art further demonstrate the method.