Two-Stage Time-Optimal Planning of Robots Along Pre-Scribed Paths with Integral Optimization of Redundancy

The problem of time-optimal planning of redundant robots is commonly solved with a decoupled two-stage approach. Starting from a task space path, at the first stage, the kinematic redundancy is locally optimized according to some performance index, then, at the second stage, the time-optimal parametrization of the resulting joint space path is performed. The performance indices to consider, as well as the redundancy resolution technique to adopt, impact the overall trajectory duration. First- or second-order Jacobian-based local redundancy resolution does not always guarantee satisfactory results at the second stage, in terms of trajectory duration, due to the choice of the initial positions, tuning of algorithm parameters, difficult joint limits management, non-convexity of the optimization problem. In this paper, we propose a global (or integral) approach for redundancy resolution, based on discrete dynamic programming, which further reduces the trajectory tracking time. To cope with the discretization of the redundancy space, the proposed methodology includes a post-processing optimization stage, aimed at smoothing the resulting joint space trajectory, guaranteeing technical feasibility. The approach is validated, in simulation, on a three-degrees-of-freedom planar robot executing two-dimensional tasks.