Minimum-jerk online planning by a mathematical programming approach

Engineering applications are often handled by means of algorithms for constrained optimization. Currently, more frequently than in the past, the need of fast solvers, which admit convergence times that are compatible with those of online applications, is strongly felt. Such need poses new additional implementation requirements, since the convergence of the mathematical programming algorithms is no more sufficient to allow for their use, but, conversely, such convergence must be achieved in very limited times. This paper proposes an efficient approach for a constrained minimum-jerk online planning problem. In particular, the considered robotic application imposes to account for time, distance, velocity and acceleration constraints. The proposed approach returns good quality solutions by admitting execution times which meet the online requirements. Comparisons with a previously adopted strategy are proposed.