We accept this thesis as conforming

Figure 1: Real-time physics-based character simulation with our framework. (a) A single controller for a planar biped responds to unanticipated changes in terrain. (b) A walk controller reconstructed from motion capture data responds to a 350N,0.2s diagonal push to the torso. Physics-based simulation and control of biped locomotion is difficult because bipeds are unstable, underactuated, high-dimensional dynamical systems. We develop a simple control strategy that can be used to generate a large variety of gaits and styles in real-time, including walking in all directions (forwards, backwards, sideways, turning), running, skipping, and hopping. Controllers can be authored using a small number of parameters, or their construction can be informed by motion capture data. The controllers are applied to 2D and 3D physically-simulated character models. Their robustness is demonstrated with respect to pushes in all directions, unexpected steps and slopes, and unexpected variations in kinematic and dynamic parameters. Direct transitions between controllers are demonstrated as well as parameterized control of changes in direction and speed. Feedback-error learning is applied to learn predictive torque models, which allows for the low-gain control that typifies many natural motions as well as producing smoother simulated motion. 1

We demonstrate a real-time simulation system capable of automatically balancing a standing character, while at the same time tracking a reference motion and responding to external perturbations. The system is general to non-human morphologies and results in natural balancing motions employing the entire body (for example, wind-milling). Our novel balance routine seeks to control the linear and angular momenta of the character. We demonstrate how momentum is related to the center of mass and center of pressure of the character and derive control rules to change these centers for balance. The desired momentum changes are reconciled with the objective of tracking the reference motion through an optimization routine which produces target joint accelerations. A hybrid inverse/forward dynamics algorithm determines joint torques based on these joint accelerations and the ground reaction forces. Finally, the joint torques are applied to the free-standing character simulation. We demonstrate results for following both motion capture and keyframe data as well as both human and non-human morphologies in presence of a variety of conditions and disturbances.

We describe an automatic technique for generating the motion of tendons and muscles under the skin of a traditionally animated character. This is achieved by integrating the traditional animation pipeline with a novel biomechanical simulator capable of dynamic simulation with complex routing constraints on muscles and tendons. We also describe an algorithm for computing the activation levels of muscles required to track the input animation. We demonstrate the results with several animations of the human hand.

Figure 1: Our biomechanical system comprises a skeleton, muscles, neural control system, and expressive face. 1

Animating natural human motion in dynamic environments is difficult because of complex geometric and physical interactions. Simulation provides an automatic solution to parts of this problem, but it needs control systems to produce lifelike motions. This paper describes the systematic computation of controllers that can reproduce a range of locomotion styles in interactive simulations. Given a reference motion that describes the desired style, a derived control system can reproduce that style in simulation and in new environments. Because it produces high-quality motions that are both geometrically and physically consistent with simulated surroundings, interactive animation systems could begin to use this approach along with more established kinematic methods.

Figure 1: Real-time control ensures fixed simulation outcome regardless of runtime user forces: First: the rest configuration of the “T”-shape structure and the two target balls. Second: reference motion from an external simulator; the two ends of the “T ” impact the two balls. Third: user-perturbed real-time simulation, without control. The two ends miss the target. Fourth: controlled user-perturbed real-time simulation, with gentle control forces, tracks the reference motion and successfully impacts the target. The perturbation force load (green arrow; applied 1/5 through the simulation, only in the third and fourth motion) pushes the “T ” in the opposite direction of motion. Recent advances have brought real-time physically based simulation within reach, but simulations are still difficult to control in real time. We present interactive simulations of passive systems such as deformable solids or fluids that are not only fast, but also directable: they follow given input trajectories while simultaneously reacting to user input and other unexpected disturbances. We achieve such directability using a real-time controller that runs in tandem with a real-time physically based simulation. To avoid stiff and overcontrolled systems where the natural dynamics are overpowered, the injection of control forces has to be minimized. This search for gentle forces can be made tractable in real-time by linearizing the system dynamics around the input trajectory, and then using a time-varying linear quadratic regulator to build the controller. We show examples of controlled complex deformable solids and fluids, demonstrating that our approach generates a requested fixed outcome for reasonable user inputs, while simultaneously providing runtime motion variety.

Dynamic simulation is a promising complement to kinematic motion synthesis, particularly in cases where simulated characters need to respond to unpredictable interactions. Moving beyond simple rag-doll effects, though, requires dynamic control. The main issue with dynamic control is that there are no standardized techniques that allow an animator to precisely specify the timing of the motion while still providing natural response to external disturbances. The few proposed techniques that address this problem are based on heuristically or manually tuning proportional-derivative (PD) control parameters and do not generalize easily. We propose an approach to dynamic character control that is able to honor timing constraints, to provide naturallooking motion and to allow for realistic response to perturbations. Our approach uses traditional PD control to interpolate between key-frames. The key innovation is that the parameters of the PD controllers are computed for each joint analytically. By continuously updating these parameters over time, the controller is able to respond naturally to both external perturbations and changes in the state of the character.

This paper presents a technique to enhance a kinematically controlled virtual character with a generic class of dynamic responses to small perturbations. Given an input motion sequence, our technique can synthesize reactive motion to arbitrary external forces with a specific style customized to the input motion. Our method re-parameterizes the motion degrees of freedom based on joint actuations in the input motion. By only enforcing the equations of motion in the less actuated coordinates, our approach can create physically responsive motion based on kinematic pose control without explicitly computing the joint actuations. We demonstrate the simplicity and robustness of our technique by showing a variety of examples generated with the same set of parameters. Our formulation focuses on the type of perturbations that significantly disrupt the upper body poses and dynamics, but have limited effect on the whole-body balance state.

Real-time adaptation of a motion capture sequence to virtual environments with physical perturbations requires robust control strategies. This paper describes an optimal feedback controller for motion tracking that allows for on-the-fly re-planning of long-term goals and adjustments in the final completion time. We first solve an offline optimal trajectory problem for an abstract dynamic model that captures the essential relation between contact forces and momenta. A feedback control policy is then derived and used to simulate the abstract model online. Simulation results become dynamic constraints for online reconstruction of full-body motion from a reference. We applied our controller to a wide range of motions including walking, long stepping, and a squat exercise. Results show that our controllers are robust to large perturbations and changes in the environment.