Energy Optimal Obstacle Avoidance Motion Planning for Wheeled Mobile Robots

Energy optimal motion planning of a wheeled mobile robot with a circular obstacle is addressed in this article. The trajectory planning problem is posed as an optimal control problem with state inequality constraint where the benchmark
$\mathcal{L}^{2}$
norm of the control inputs is considered as the cost function. The necessary conditions for optimality are formally derived using the variational principle and the fact that the control inputs remain continuous at the time instant of entering the constraint boundary is proven. The necessary conditions permit decomposing the problem in two intervals: prior to and after activation of the constraint. Parametric studies are conducted to study the impact of the size of the obstacle of the optimal trajectory of the wheeled mobile robot.