This paper develops methods for determining a visually appealing length for a motion transition, i.e., a segue between two sequences of character animation. Motion transitions are an important component in generating compelling animation streams in virtual environments and computer games. For reasons of efficiency and speed, linear interpolation is often used as the transition method, where the motion is blended between specified start and end frames. The blend length of a transition using this technique is critical to the visual appearance of the motion. Two methods for determining an optimal blend length for such transitions are presented. These methods are suited to different types of motion. They are empirically evaluated through user studies. For the motions tested, we find (1) that visually pleasing transitions can be generated using our optimal blend lengths without further tuning of the blending parameters; and (2), that users prefer these methods over a generic fixed-length blend.

This paper presents a novel constraint-based motion editing technique. On the basis of animator-specified kinematic and dynamic constraints, the method converts a given captured or animated motion to a physically plausible motion. In contrast to previous methods using spacetime optimization, we cast the motion editing problem as a constrained state estimation problem based on the per-frame Kalman filter framework. The method works as a filter that sequentially scans the input motion to produce a stream of output motion frames at a stable interactive rate. Animators can tune several filter parameters to adjust to different motions, or can turn the constraints on or off based on their contributions to the final re- sult. One particularly appealing feature of the proposed technique is that animators find it very scalable and intuitive. Experiments on various systems show that the technique processes the motions of a human with 54 degrees of freedom at about 150 fps when only kinematic constraints are applied, and at about 10 fps when both kinematic and dynamic constraints are applied. Experiments on various types of motion show that the proposed method produces remarkably realistic animations.

Motion capture has become a premiere technique for animation of humanlike characters. To facilitate its use, researchers have focused on the manipulation of data for retargeting, editing, combining, and reusing motion capture libraries. In many of these efforts joint angle plus root trajectories are used as input, although this format requires an inherent mapping from the raw data recorded by many popular motion capture set-ups. In this paper, we propose a novel solution to this mapping problem from 3D marker position data recorded by optical motion capture systems to joint trajectories for a fixed limb-length skeleton using a forward dynamic model. To accomplish the mapping, we attach virtual springs to marker positions located on the appropriate landmarks of a physical simulation and apply resistive torques to the skeleton's joints using a simple controller. For the motion capture samples, joint-angle postures are resolved from the simulation's equilibrium state, based on the internal torques and external forces. Additional constraints, such as foot plants and hand holds, may also be treated as addition forces applied to the system and are a trivial and natural extension to the proposed technique. We present results for our approach as applied to several motion-captured behaviors.

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.

Many popular motion editing methods do not take physical principles into account potentially producing implausible motions. This paper introduces an efficient method for touching up edited motions to improve physical plausibility. We start by estimating a mass distribution consistent with reference motions known to be physically correct. The edited motion is then divided into ground and flight stages and adjusted to enforce appropriate physical laws for, respectively, zero moment point (ZMP) constraints and correct ballistic trajectory. Unlike previous methods, we do not solve a nonlinear optimization to calculate the adjustment. Instead, closed-form methods are used to construct a hierarchical displacement map which sequentially refines userspecified degrees of freedom at different scales. This is combined with standard methods for kinematic constraint enforcement, yielding an efficient and scalable editing method that allows users to model real human behaviors. The potential of our approach is demonstrated in a number of examples.

Figure 1: The biomechanical model in action. A motion controller drives the musculoskeletal system toward a sequence of target poses. We introduce a comprehensive biomechanical model of the human upper body. Our model confronts the combined challenge of modeling and controlling more or less all of the relevant articular bones and muscles, as well as simulating the physics-based deformations of the soft tissues. Its dynamic skeleton comprises 68 bones with 147 jointed degrees of freedom, including those of each vertebra and most of the ribs. To be properly actuated and controlled, the skeletal submodel requires comparable attention to detail with respect to muscle modeling. We incorporate 814 muscles, each of which is modeled as a piecewise uniaxial Hill-type force actuator. To simulate biomechanically realistic flesh deformations, we also develop a coupled finite element model with the appropriate constitutive behavior, in which are embedded the detailed 3D anatomical geometries of the hard and soft tissues. Finally, we develop an associated physics-based animation controller that computes the muscle activation signals necessary to drive the elaborate musculoskeletal system in accordance with a sequence of target poses specified by an animator.

Figure 1: Tracking enables artistic expression and physical simulation to work hand-in-hand, as demonstrated in our animation of a character’s unfortunate event. We begin (left to right) with the artist’s animation, automatically generate a set of Petrov-Galerkin test functions (visualized as colored patches), and then solve the constrained Lagrangian mechanics equations to flesh out wrinkles and folds. We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist’s animated character to guiding a simulated inanimate object.

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.

(a) A forward roll transformed to a dive roll. (b) A cartwheel retargeted to an Asimo-like robot. (c) A walk transformed onto a balance beam. Figure 1: Physically based motion transformation and retargeting. Human motions are the product of internal and external forces, but these forces are very difficult to measure in a general setting. Given a motion capture trajectory, we propose a method to reconstruct its open-loop control and the implicit contact forces. The method employs a strategy based on randomized sampling of the control within user-specified bounds, coupled with forward dynamics simulation. Sampling-based techniques are well suited to this task because of their lack of dependence on derivatives, which are difficult to estimate in contact-rich scenarios. They are also easy to parallelize, which we exploit in our implementation on a compute cluster. We demonstrate reconstruction of a diverse set of captured motions, including walking, running, and contact rich tasks such as rolls and kip-up jumps. We further show how the method can be applied to physically based motion transformation and retargeting, physically plausible motion variations, and referencetrajectory-free idling motions. Alongside the successes, we point out a number of limitations and directions for future work. 1

Abstract—We present a physics-based approach to generate 3D biped character animation that can react to dynamical environments in real time. Our approach utilizes an inverted pendulum model to online adjust the desired motion trajectory from the input motion capture data. This online adjustment produces a physically plausible motion trajectory adapted to dynamic environments, which is then used as the desired motion for the motion controllers to track in dynamics simulation. Rather than using Proportional-Derivative controllers whose parameters usually cannot be easily set, our motion tracking adopts a velocity-driven method which computes joint torques based on the desired joint angular velocities. Physically correct full-body motion of the 3D character is computed in dynamics simulation using the computed torques and dynamical model of the character. Our experiments demonstrate that tracking motion capture data with real-time response animation can be achieved easily. In addition, physically plausible motion style editing, automatic motion transition, and motion adaptation to different limb sizes can also be generated without difficulty. Index Terms—3D human motion, physics-based simulation, biped walk and balance, motion capture data. Ç 1