Previous work by the authors has shown that temporal finite element approximations can be used for the representation of targeted optimal control problems, and that a weak equilibrium formulation leads to robust and efficient simulations. A free-time formulation is now introduced to increase the degree of freedom in finding optimal movement. The timescale parameter in relation to the objective function is discussed and verified by numerical examples. For movements with partial contact multiple phases with different mechanical properties are included. The free-time formulation allows these phases to be determined by the optimization. A three-phase two-foot high jump is simulated where the movement optimization finds a prior motion preparing for the subsequent phases with different mechanical properties.
QC 20140423