Physics-based character locomotion control with large simulation time steps.

Abstract

Physical simulated locomotion allows rich and varied interactions with environments and other characters. However, control is di cult due to factors such as a typical character's numerous degrees of freedom and small stability region, discontinuous ground contacts, and indirect control over the centre of mass. Previous academic work has made signi cant progress in addressing these problems, but typically uses simulation time steps much smaller than those suitable for games. This project deals with developing control strategies using larger time steps. After describing some introductory work showing the di culties of implementing a handcrafted controller with large physics time steps, three major areas of work are discussed. The rst area uses trajectory optimization to minimally alter reference motions to ensure physical validity, in order to improve simulated tracking. The approach builds on previous work which allows ground contacts to be modi ed as part of the optimization process, extending it to 3D problems. Incorporating contacts introduces di cult complementarity constraints, and an exact penalty method is shown here to improve solver robustness and performance compared to previous relaxation methods. Trajectory optimization is also used to modify reference motions to alter characteristics such as timing, stride length and heading direction, whilst maintaining physical validity, and to generate short transitions between existing motions. The second area uses a sampling-based approach, previously demonstrated with small time steps, to formulate open loop control policies which reproduce reference motions. As a prerequisite, the reproducibility of simulation output from a common game physics engine, PhysX, is examined and conditions leading to highly reproducible behaviour are determined. For large time steps, sampling is shown to be susceptible to physical inva- lidities in the reference motion but, using physically optimized motions, is successfully applied at 60 time steps per second. Finally, adaptations to an existing method using evolutionary algorithms to learn feedback policies are described. With large time steps, it is found to be necessary to use a dense feedback formulation and to introduce phase-dependence in order to obtain a successful controller, which is able to recover from impulses of several hundred Newtons applied for 0.1s. Additionally, it is shown that a recent machine learning approach based on support vector machines can identify whether disturbed character states will lead to failure, with high accuracy (99%) and with prediction times in the order of microseconds. Together, the trajectory optimization, open loop control, and feedback developments allow successful control for a walking motion at 60 time steps per second, with control and simulation time of 0.62ms per time step. This means that it could plausibly be used within the demanding performance constraints of games. Furthermore, the availability of rapid failure prediction for the controller will allow more high level control strategies to be explored in future.