Thesis Proposal: Gait Synthesis with Spacetime Optimization

The current state of computer animation shows that the automatic synthesis of physically realistic motion is an extremely difficult problem. Despite several diverse approaches to this problem, such as inverse dynamics and forward simulation, character animation is still almost always created by hand or, less commonly, through motion capture. Within the last decade, spacetime optimization has arisen as an alternate tool for the creation of physically realistic characters animation. While offering many advantages over other synthesis methods, spacetime optimization has not yet been applied to problems of interesting size. This difficulty lies primarily in the mathematical methods currently used to solve the optimization problem that the spacetime formulation presents. In my thesis, I propose to explore a set of spacetime optimization problems and to develop a better method of solving these problems than is offered by the current literature. The set of problems I will investigate is that of the synthesis of legged locomotion for a single walk-cycle on level, obstacle-free terrain. The first part of this thesis will involve exploring the field of optimization for a method which performs better than the state of the art. This gain may either be in the form of an improved numerical method or a heuristic, specific to the domain of legged locomotion, that provides better initial guesses at the solution and hence faster convergence. The second part of my thesis will involve applying this improved optimization technique to the problem of gait synthesis. 1 Problem Definition Despite the often striking visual differences between computer animation and traditional “pen and ink” animation, their underlying techniques of character1 animation remain fundamentally the same. In both mediums, the vast majority of this work is 1“Character” in this paper is a general term used to refer to any active object that is being animated. A “character” therefore can be a literal human character, an animal, a machine, or any other complex, dynamic entity.