Locomotion Synthesis Methods for Humanoid Characters

This thesis introduces locomotion synthesis methods for humanoid characters. Motion synthesis is an under-constrained problem that requires additional constraints beyond user inputs. Two main approaches to introducing additional constraints are physics-based and data-driven. Despite significant progress in the past 20 years, major difficulties still exist for both approaches. In general, building animation systems that are flexible to user requirements while keeping the synthesized motions plausible remain a challenging task. The methods introduced in this thesis, presented in two-parts, aim to allow animation systems to be more flexible to user demands without radically violating constraints that are important for maintaining plausibility. In the first part of the thesis, we address an important subproblem in physics-based animation --- controller synthesis for humanoid characters. We describe a method for optimizing the parameters of a physics-based controller for full-body, 3D walking. The objective function includes terms for power minimization, angular momentum minimization, and minimal head motion, among others. Together these terms produce a number of important features of natural walking, including active toe-off, near-passive knee swing, and leg extension during swing. We then extend the algorithm to optimize for robustness to uncertainty. Many unknown factors, such as external forces, control torques, and user control inputs, cannot be known in advance and must be treated as uncertain. Controller optimization entails optimizing the expected value of the objective function, which is computed by Monte Carlo methods. We demonstrate examples with a variety of sources of uncertainty and task constraints. The second part of this thesis deals with the data-driven approach and the problem of motion modeling. Defining suitable models for human motion data is non-trivial. Simple linear models are not expressive enough, while more complex models require setting many parameters and are difficult to learn with limited data. Using Bayesian methods, we demonstrate how the Gaussian process prior can be used to derive a kernelized version of multilinear models. The result is a locomotion model that takes advantage of training data addressed by multiple indices to improve generalization to unseen motions.Ph