MOTION DYNAMICS AND OPTIMIZATION OF HUMANS AND A BIOLOGICALLY INSPIRED BIPED ROBOT

In this talk, models,methods and results for numerical optimization of human motions will be discussed. Furthermore, a short overview of motion optimization of a biologically inspired biped robot will be given. Both legged robots and humans consist of tree structured systems of joints and links. Classic legged robots are usually driven by one motor per joint; humans are driven by muscles, there are usually more than one or two muscles per joints and some muscles span more than one joint. Classical robots are designed to be as stiff as possible to simplify control, while the human motion apparatus shows a high amount of natural compliance. Forward dynamics models of multibody systems like robots or the human motion apparatus consist of differential (algebraic) equations that compute the acceleration for each of the joints from the joint angles and velocities and the controls. The controls for legged robots can be e.g. motor torques, while for the biomechanical systems the controls are the muscle activations that (by additional models for the dynamics of muscle activation) lead to the force exertion. A fixed motion goal for a robot may be realized by usually infinitely many joint angle trajectories, and for human motions, even a fixed joint angle trajectory may be realized by infinitely many muscle acti- vation trajectories. These redundancies allow to chose from infinitely many possible motor torque resp. muscle activation trajectories for one specific motion or motion goal; optimization and optimal con- trol (with an appropriate objective function like velocity, energy consumption or stability) are common ways to overcome and profit from these redundancies. Solving optimal control problems for legged robot and human motion involves evaluation of the multi- body system dynamics several times. The efficient Articulated Body Algorithm, which is adapted to the special (tree) structure of the systems is used. Efficient numerical optimal control techniques have been adapted to the problems and by using direct collocation (which discretizes both states and controls and therefore allows for solving the optimal control problem and integrating the differential equations of motion in one optimization problem) instead of widely used control parameterization approaches (which have to integrate the differential equations of motion several time to gain derivative information