A via-point time optimization algorithm for complex sequential trajectory formation.

In our previous research, we proposed a method for the reproduction of complex movement trajectories and robot arm control that could mimic fast, skilled human movements. That method is based on bi-directional theory and uses a representation of a set of via-points as boundary conditions or control variables to perform robot arm trajectory control. The via-points are extracted from human movement data and the resultant via-point representation is able to regenerate handwritten characters, control a Kendama toy, and perform a tennis serve. The via-point information contains both spatial and temporal information, that is, the position on the trajectory and the time of passing through the via-point position, respectively. Trajectory generation is performed using the trajectory formation model based on the optimal criterion, namely, the smoothness criterion, for which the boundary conditions are both the position and the timing of the via-point information. However, generating a smooth trajectory at different movement speeds is quite difficult if the time of passing through the via-point position is unknown or different from the extracted via-point time. In this paper, we therefore propose a new algorithm which can determine temporal via-point information. Our proposed algorithm can generate roughly the same trajectory as the measured human trajectory from only the spatial information of via-point locations. The optimality and the convergence of the new algorithm are investigated theoretically, and the trajectory generated by the algorithm is shown in numerical experiments. It is shown that starting from arbitrary temporal information the proposed algorithm can produce an appropriate trajectory.