Physically based simulation of human motions is an important issue in the context of computer animation, robotics and biomechanics. We present a new technique for allowing our physically-simulated planar biped characters to imitate human behaviors. Our contribution is twofold. We developed an optimization method that transforms any (either motion-captured or kinematically synthesized) biped motion into a physically-feasible, balance-maintaining simulated motion. Our optimization method allows us to collect a rich set of training data that contains stylistic, personality-rich human behaviors. Our controller learning algorithm facilitates the creation and composition of robust dynamic controllers that are learned from training data. We demonstrate a planar articulated character that is dynamically simulated in real time, equipped with an integrated repertoire of motor skills, and controlled interactively to perform desired motions.

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.

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.

This paper describes a method for optimizing the parameters of a physics-basedcontrollerforfull-body,3Dwalking. AmodifiedversionoftheSIMBICONcontroller[Yinetal.2007]isoptimizedfor characters of varying body shape, walking speed and step length. 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 featuresofnaturalwalking,includingactivetoe-off,near-passiveknee swing, and leg extension during swing. We explain the specific formofourobjectivecriteria,andshowtheimportanceofeachterm towalkingstyle. Wedemonstrateoptimizedcontrollersforwalking withdifferentspeeds,variationinbodyshape,andingroundslope. Keywords: Physics-based animation, controller synthesis, human motion, optimization. 1

In late 2006, Nintendo released a new game controller, the Wiimote, which included a three-axis accelerometer. Since then, a large variety of novel applications for these controllers have been developed by both independent and commercial developers. We add to this growing library with three performance interfaces that allow the user to control the motion of a dynamically simulated, animated character through the motion of his or her arms, wrists, or legs. For comparison, we also implement a traditional joystick/button interface. We assess these interfaces by having users test them on a set of tracks containing turns and pits. Two of the interfaces (legs and wrists) were judged to be more immersive and were better liked than the joystick/button interface by our subjects. All three of the Wiimote interfaces provided better control than the joystick interface based on an analysis of the failures seen during the user study.

Figure 1: Our data-driven controller allows the physically-simulated biped character to reproduce challenging motor skills captured in motion data. We present a dynamic controller to physically simulate under-actuated three-dimensional full-body biped locomotion. Our data-driven controller takes motion capture reference data to reproduce realistic human locomotion through realtime physically based sim-ulation. The key idea is modulating the reference trajectory con-tinuously and seamlessly such that even a simple dynamic tracking controller can follow the reference trajectory while maintaining its balance. In our framework, biped control can be facilitated by a large array of existing data-driven animation techniques because our controller can take a stream of reference data generated on-the-fly at runtime. We demonstrate the effectiveness of our approach through examples that allow bipeds to turn, spin, and walk while steering its direction interactively.

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.

Figure 1: Real-time physics-based simulation of walking. The method provides robust control across a range of gaits, styles, characters, and skills. Motions are easily authored by novice users. We present a control strategy for physically-simulated walking motions that generalizes well across gait parameters, motion styles, character proportions, and a variety of skills. The control is realtime, requires no character-specific or motion-specific tuning, is robust to disturbances, and is simple to compute. The method works by integrating tracking, using proportional-derivative control; foot placement, using an inverted pendulum model; and adjustments for gravity and velocity errors, using Jacobian transpose control. Highlevel gait parameters allow for forwards-and-backwards walking, various walking speeds, turns, walk-to-stop, idling, and stop-towalk behaviors. Character proportions and motion styles can be authored interactively, with edits resulting in the instant realization of a suitable controller. The control is further shown to generalize across a variety of walking-related skills, including picking up objects placed at any height, lifting and walking with heavy crates, pushing and pulling crates, stepping over obstacles, ducking under obstacles, and climbing steps. 1

Figure 1: A biped (left) performs a 180 ◦ turn and then walks backwards on uneven terrain and (right) climbs up stairs. We describe a framework for the automatic synthesis of biped locomotion controllers that adapt to uneven terrain at run-time. The framework consists of two components: a per-footstep end-effector path planner and a per-timestep generalized-force solver. At the start of each footstep, the planner performs short-term planning in the space of end-effector trajectories. These trajectories adapt to the interactive task goals and the features of the surrounding uneven terrain at run-time. We solve for the parameters of the planner for different tasks in offline optimizations. Using the per-footstep plan, the generalized-force solver takes ground contacts into consideration and solves a quadratic program at each simulation timestep to obtain joint torques that drive the biped. We demonstrate the capabilities of the controllers in complex navigation tasks where they perform gradual or sharp turns and transition between moving forwards, backwards, and sideways on uneven terrain (including hurdles and stairs) according to the interactive task goals. We also show that the resulting controllers are capable of handling morphology changes to the character.

Abstract — This paper presents a model-based method, called