A simple control policy for achieving minimum jerk trajectories

Point-to-point fast hand movements, often referred to as ballistic movements, are a class of movements characterized by straight paths and bell-shaped velocity profiles. In this paper we propose a bang–bang optimal control policy that can achieve such movements. This optimal control policy is accomplished by minimizing the L∞L∞ norm of the jerk profile of ballistic movements with known initial position, final position, and duration of movement. We compare the results of this control policy with human motion data recorded with a manipulandum. We propose that such bang–bang control policies are inherently simple for the central nervous system to implement and also minimize wear and tear on the bio-mechanical system. Physiological experiments support the possibility that some parts of the central nervous system use bang–bang control policies. Furthermore, while many computational neural models of movement control have used a bang–bang control policy without justification, our study shows that the use of such policies is not only convenient, but optimal.