Jerk-limited Holonomic Robot Motion Planning Using Barrier Functions

This paper proposes a jerk-limited motion restriction algorithm to adapt a higher level single-integrator-based path planner to a constrained triple integrator robot. The algorithm guarantees that the robot never deviates from the nominal path represented by a single-integrator virtual agent by more than a predefined lateral distance. This is achieved by using an online discrete-time modification of the barrier function approach. A tracking controller's inputs are bounded based on the barrier function formulation, which ensures that dynamic constraints are met. The nominal position of the virtual agent is then advanced according to the current robot position and the barrier function value. The effectiveness of this method is demonstrated with a simulation of a quadrotor model. The quadrotor was able to track the required inputs well and keep within the predefined displacement from the nominal path with some acceptably small errors.