Cornell Ranger : Implementing energy-optimal trajectory control using low information , reflex-based control

In optimal trajectory control, one formulates an optimization problem in which one is interested in minimizing a certain criteria like, say, energy used per unit distance travelled subject to various constraints like say walking speed, no foot scuffing, respecting actuator bounds and so forth. The optimal trajectory problem is then cast into a parameter optimization by, e.g., finding control torques as a piecewise linear function of time and then optimizing using one or another numerical method. Assuming numerical convergence to a unique local minimum, a sufficiently fine grid size, usually associated with a large number of control parameters, ensures a reasonably accurate approximation to the true solution.