Jack M. Wang

Gaussian Process Dynamical Models for Human Motion

We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from high-dimensional motion capture data. A GPDM is a latent variable model. It comprises a low-dimensional latent space with associated dynamics, as well as a map from the latent space to an observation space. We marginalize out the model parameters in closed form by using Gaussian process priors for both the dynamical and the observation mappings. This results in a nonparametric 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.

Optimizing locomotion controllers using biologically-based actuators and objectives

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.

Optimizing walking controllers

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.

Multifactor Gaussian process models for style-content separation

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 persons identity, gait, and the current state of motion. We demonstrate our approach using time-series prediction, and by synthesizing novel animation from the model.

Optimizing walking controllers for uncertain inputs and environments

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.

Continuous character control with low-dimensional embeddings

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 methods 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 characters 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.

Animating human lower limbs using contact-invariant optimization

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.

Light-absorbing properties of ambient black carbon and brown carbon from fossil fuel and biomass burning sources

The optical properties of ambient black carbon-containing particles and the composition of their associated coatings were investigated at a downtown site in Toronto, Canada, for 2 weeks in June 2013. The objective was to assess the relationship between black carbon (BC) coating composition/thickness and absorption. The site was influenced by emissions from local vehicular traffic, wildfires in Quebec, and transboundary fossil fuel combustion emissions in the United States. Mass concentrations of BC and associated nonrefractory coatings were measured using a soot particle–aerosol mass spectrometer (SP-AMS), while aerosol absorption and scattering were measured using a photoacoustic soot spectrometer (PASS). Absorption enhancement was investigated both by comparing ambient and thermally denuded PASS absorption data and by relating absorption data to BC mass concentrations measured using the SP-AMS. Minimal absorption enhancement attributable to lensing at 781 nm was observed for BC using both approaches. However, brown carbon was detected when the site was influenced by wildfire emissions originating in Quebec. BC coating to core mass ratios were highest during this period (~7), and while direct absorption by brown carbon resulted in an absorption enhancement at 405 nm (>2.0), no enhancement attributable to lensing at 781 nm was observed. The efficiency of BC coating removal in the denuder decreased substantially when wildfire-related organics were present and may represent an obstacle for future similar studies. These findings indicate that BC absorption enhancement due to lensing is minimal for downtown Toronto, and potentially other urban locations, even when impacted by long-range transport events.

Predictive Simulation Generates Human Adaptations during Loaded and Inclined Walking

Predictive simulation is a powerful approach for analyzing human locomotion. Unlike techniques that track experimental data, predictive simulations synthesize gaits by minimizing a high-level objective such as metabolic energy expenditure while satisfying task requirements like achieving a target velocity. The fidelity of predictive gait simulations has only been systematically evaluated for locomotion data on flat ground. In this study, we construct a predictive simulation framework based on energy minimization and use it to generate normal walking, along with walking with a range of carried loads and up a range of inclines. The simulation is muscle-driven and includes controllers based on muscle force and stretch reflexes and contact state of the legs. We demonstrate how human-like locomotor strategies emerge from adapting the model to a range of environmental changes. Our simulation dynamics not only show good agreement with experimental data for normal walking on flat ground (92% of joint angle trajectories and 78% of joint torque trajectories lie within 1 standard deviation of experimental data), but also reproduce many of the salient changes in joint angles, joint moments, muscle coordination, and metabolic energy expenditure observed in experimental studies of loaded and inclined walking.

Erratum: "Gaussian process dynamical models for human motion" (IEEE Transactions on Pattern analysis and Machine Intelligenc (292))

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.