We present a trajectory optimization approach to animating human activities that are driven by the lower body. Our approach is based on contact-invariant optimization. We develop a simplified and generalized formulation of contact-invariant optimization that enables continuous optimization over contact timings. This formulation is applied to a fully physical humanoid model whose lower limbs are actuated by musculotendon units. Our approach does not rely on prior motion data or on task-specific controllers. Motion is synthesized from first principles, given only a detailed physical model of the body and spacetime constraints. We demonstrate the approach on a variety of activities, such as walking, running, jumping, and kicking. Our approach produces walking motions that quantitatively match ground-truth data, and predicts aspects of human gait initiation, incline walking, and locomotion in reduced gravity.

Interactive, task-guided character controllers must be agile and responsive to user input, while retaining the flexibility to be readily authored and modified by the designer. Central to a method's ease of use is its capacity to synthesize character motion for novel situations without requiring excessive data or programming effort. In this work, we present a technique that animates characters performing user-specified tasks by using a probabilistic motion model, which is trained on a small number of artist-provided animation clips. The method uses a low-dimensional space learned from the example motions to continuously control the character's pose to accomplish the desired task. By controlling the character through a reduced space, our method can discover new transitions, tractably precompute a control policy, and avoid low quality poses.

We present a technique for automatically synthesizing walking and running controllers for physically-simulated 3D humanoid characters. The sagittal hip, knee, and ankle degrees-of-freedom are actuated using a set of eight Hill-type musculotendon models in each leg, with biologically-motivated control laws. The parameters of these control laws are set by an optimization procedure that satisfies a number of locomotion task terms while minimizing a biological model of metabolic energy expenditure. We show that the use of biologically-based actuators and objectives measurably increases the realism of gaits generated by locomotion controllers that operate without the use of motion capture data, and that metabolic energy expenditure provides a simple and unifying measurement of effort that can be used for both walking and running control optimization.

We introduce methods for optimizing physics-based walking controllers 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. These variables are represented with probability distributions, and a return function scores the desirability of a single motion. Controller optimization entails maximizing the expected value of the return, which is computed by Monte Carlo methods. We demonstrate examples with different sources of uncertainty and task constraints. Optimizing control strategies under uncertainty increases robustness and produces natural variations in style.

This paper describes a method for optimizing the parameters of a physics-based controller for full-body, 3D walking. A modified version of the SIMBICON controller [Yin et al. 2007] is optimized for 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 features of natural walking, including active toe-off, near-passive knee swing, and leg extension during swing. We explain the specific form of our objective criteria, and show the importance of each term to walking style. We demonstrate optimized controllers for walking with different speeds, variation in body shape, and in ground slope.

We introduce Gaussian process dynamical models (GPDM) for nonlinear time series analysis, with applications to learning models of human pose and motion from high-dimensionalmotion capture data. A GPDM is a latent variable model. It comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space. We marginalize out the model parameters in closed-form, using Gaussian process priors for both the dynamics and the observation mappings. This results in a non-parametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach, and compare four learning algorithms on human motion capture data in which each pose is 50-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces.

In the above titled paper (ibid., vol. 30, no. 2, pp. 283-298, Feb 08), two figures were misprinted. The correct figures are presented here.

We introduce models for density estimation with multiple, hidden, continuous factors. In particular, we propose a generalization of multilinear models using nonlinear basis functions. By marginalizing over the weights, we obtain a multifactor form of the Gaussian process latent variable model. In this model, each factor is kernelized independently, allowing nonlinear mappings from any particular factor to the data. We learn models for human locomotion data, in which each pose is generated by factors representing the person's identity, gait, and the current state of motion. We demonstrate our approach using time-series prediction, and by synthesizing novel animation from the model.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space. We marginalize out the model parameters in closed-form, using Gaussian Process (GP) priors for both the dynamics and the observation mappings. This results in a nonparametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach on human motion capture data in which each pose is 62-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces. Webpage: http://www.dgp.toronto.edu/