Motion Planning with Obstacle Avoidance for Wheeled Inverted Pendulum System Based on PMP Approach
Anil B, Sneha Gajbhiye · 2023
This work is mainly focused on the optimal motion planning problem of a Wheeled Inverted Pendulum (WIP) system, which is one of the benchmark mechanical systems used for the study of nonholonomic systems. Designing motion planning control law while respecting the nonholonomic constraints possesses a challenging control problem. We address the problem where the given system has to reach any desired target configuration from an arbitrary initial configuration by finding an optimal path which takes into account the path curvature, control effort as well as obstacles in the environment. Throughout the course of motion, it is desirable to maintain the pendulum body at the upright position. To tackle this problem from a variational point of view, Pontryagin's Minimum Prin-ciple (PMP) is utilized for deriving the necessary optimality conditions which finds a collision free optimal path with a reduced control cost satisfying the path smoothness constraints defined via an objective function. Numerical simulations are carried out on the derived nonlinear WIP model to validate the proposed theoretical results.