ABSTRACT

Numerical Solution of a Hamilton-Jacobi-Bellman Equation and its Application to Animation.

Gideon Amos, UCL

The trouble with computer animation of humans and other animals, is that realistic motion and interactivity rarely go together. We are developing a method that may go part way towards solving this problem. Starting with a dynamic model of a simple 'toy' creature, the method generates a feedback controller for stationary or repetitive behaviours. Together, the dynamic model and controller can generate globally optimal trajectories at interactive rates. The method solves a first order partial differential equation, a Hamilton-Jacobi-Bellman equation, the solution of which exists only in a specific sense. It is the continuous state equivalent of a dynamic programming solution and is also a form of reinforcement learning. The overwhelming limitation of this method is that the cost of the solution scales exponentially with the number of degrees of freedom of the dynamic model. A kd-tree based adaptive meshing stragegy is employed to improve the scalability. We hope to demonstrate that this method can produce realistic and engaging interactive animations.

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