Safe Receding Horizon Motion Planning with Infinitesimal Update Interval

Safety verification in motion planning is known to be computationally burdensome, despite its importance in robotics. In this paper, we investigate the behavior of safe receding horizon motion planners when the update interval becomes infinitesimal. By requiring the trajectory parameters to evolve continuously in time, the trajectory optimization problem is reformulated into a time-derivative form, whose decision variables are their rate of change. This results in a quadratic programming problem which directly provides safe input, and can be regarded as a real-time safety filter. The input expressivity is also enhanced by leveraging the differentiable structure of the parameter space. The proposed safety filter is experimentally validated using a wheeled ground robot in obstacle-cluttered environments. The result shows that the safety filter is capable of generating safe inputs in real-time, while addressing hundreds of constraints simultaneously.