Matebese, BelindaWithey, DanielBanda, M.K. (Mapundi)2018-11-152018-03Matebese B., Withey D., Banda M.K. (2018) Modified Newton’s Method in the Leapfrog Method for Mobile Robot Path Planning. In: Dash S., Naidu P., Bayindir R., Das S. (eds) Artificial Intelligence and Evolutionary Computations in Engineering Systems. Advances in Intelligent Systems and Computing, vol 668, pp. 71-78. Springer, Singapore.2194-5357 (print)2194-5365 (online)10.1007/978-981-10-7868-2_7http://hdl.handle.net/2263/67266The problem of determining an optimal trajectory for an autonomous mobile robot in an environment with obstacles is considered. The Leapfrog approach is used to solve the ensuing system of equations derived from the first-order optimality conditions of the Pontryagin’s Minimum Principle. A comparison is made between a case in which the classical Newton Method and the Modified Newton Method are used in the shooting method for solving the two-point boundary value problem in the inner loop of the Leapfrog algorithm. It can be observed that with this modification there is an improvement in the convergence rate of the Leapfrog algorithm in general.en© Springer Nature Singapore Pte Ltd. 2018. The original publication is available at http://www.springer.comseries/11156.Evolutionary algorithmsTwo point boundary value problemsOptimal trajectoriesNewton algorithmFirst-order optimality conditionAutonomous mobile robotRobot programmingNewton-Raphson methodMotion planningMobile robotsCollision avoidanceBoundary value problemsTrajectory planningObstacle avoidanceLeapfrog algorithmPontryagin’s minimum principleModified Newton algorithmPostprint Article