Time Optimal Trajectory Planning for a Robotic Manipulator Using an Improved Hippopotamus Optimization Algorithm

An improved Hippopotamus Optimization (IHO) algorithm is proposed to address the uneven initial population distribution and susceptibility to local optima of standard Hippopotamus Optimization (HO) in time-optimal trajectory planning for robotic manipulators.The algorithm combines Latin hypercube sampling, a nonlinear variable-step strategy, and stagnation-triggered genetic mutation.Latin hypercube sampling improves the uniformity of the initial population, the nonlinear variable-step strategy balances global exploration and local exploitation, and genetic mutation is activated when the search stagnates.Quintic B-splines are used to construct the joint trajectories of a UR5e manipulator.Segment durations are optimized to minimize the total motion time subject to joint velocity and acceleration constraints.Benchmark-function tests and trajectory-planning simulations are conducted to evaluate the proposed method.Compared with standard HO, particle swarm optimization, and a genetic algorithm, IHO achieves the shortest motion time, faster convergence, and the best run-to-run stability among the tested methods while satisfying the prescribed kinematic constraints.