Optimal Trajectory Generation for a Robotic Worm via Parameterization by B-Spline Curves

In this paper we intend to generate some set of optimal trajectories according to the number of control points has been applied for parameterizing those using B-spline curves. The trajectories are used to generate an optimal locomotion gait in a crawling worm-like robot. Due to gait design considerations it is desired to minimize the required torques in a cycle of gait. Similar to caterpillars, progress in our crawling robot is achieved by propagating a trapezoidal wave from tail to head in the vertical plane. According to this model, the optimization problem has been solved via parameterization of joint trajectories, and consequently cost function, using cubic B-spline curves versus variant numbers of control points (CPs) needed in building those. Indeed, it is tried to find the best number of the CPs, of which the cost function obtains a minimum dynamical effort. To this end, the Genetic Algorithm is employed to find the minimal cost value once a nominated number of CPs is considered. Furthermore, since a complete period of this locomotion gait is composed of separated stages called sub-motions, thus the optimal trajectories for each sub-motion is examined independently. The results show choosing the number of CPs between 8 to 12 points constructs the optimized trajectories that reduce the dynamical effort of crawl in comparison with ones are reported by previous researches.