Recursive dynamics and optimal control techniques for human motion planning

Techniques for simulating dynamically correct human movements are becoming increasingly important in medical, military, graphics and space-exploration applications. In this thesis, we develop an efficient optimal control based approach to this problem.; We model virtual humans as a kinematic chain consisting of serial, closed-loop, and tree-structures. We first experimented with a Lagrangian approach employing a recursive root finding technique and applied it to the problem of human ladder climbing. However, the Lagrange's method has several limitations: (1) it does not scale well with increasing number of degrees of freedom of a figure model; (2) it is error-prone since the re-formulation of the dynamic equations is necessary for different articulated figures; (3) it is cumbersome in treating complex figure topology. To overcome these limitations and to include knowledge from biomechanical studies, we have developed an efficient minimum-torque motion planning method. This new method is based on the use of optimal control theory within a recursive dynamics framework. Recursive dynamics computation has been shown to allow efficient simulation of systems with large degrees of freedom regardless of their topology. It obviates the need for the reformulation of the dynamic equations for different articulated figures.; We then use a quasi-Newton method based nonlinear programming technique to solve our minimal torque-based human motion planning problem. This method achieves superlinear convergence. We use the screw theoretical method to compute analytically the necessary gradient of the motion and force. This provides a better conditioned optimization computation and allows the robust and efficient implementation of our method. Cubic spline functions have been used to make the search space for an optimal solution finite. In addition, our approach is suitable for implementation using an object-oriented programming language.; We demonstrate the efficacy of our proposed method based on a variety of human motion tasks involving open and closed loop kinematic chains. Our models are built using parameters chosen from an anthropomorphic database. Simulations are presented to validate our approach. These include a variety of human activity simulations to show the robustness of the method in various environments. The value of the method is justified by the natural looking and the physically correct motions that can be synthesized.