Density Functions for Dynamic Safe Navigation of Robotic Systems

This paper presents a novel density function-based approach for safe navigation in dynamic environments with time-varying obstacles and targets. We analytically construct time-varying density functions to tackle the challenges of dynamic safe navigation. Leveraging this framework, we develop a safe feedback controller that guarantees both safety and convergence to the target from almost all initial conditions w.r.t Lebesgue measure. The effectiveness of our approach is demonstrated on complex robotic systems, including the safe navigation of a quadruped robot in the presence of time-varying obstacles and sensor uncertainty, as well as a robotic arm tracking a time-varying target amidst static obstacles.