# Projects

## System Dynamics

We have developed dynamic models and designs for vehicles, biomechatronics, robots, pianos, machines, and sports equipment. Deriving the kinematic and dynamic equations for such 3D multibody systems is tedious and error-prone, so we use linear graph theory and symbolic computing to develop formulations that automatically generate the equations of motion. Graph theory provides a unified approach for multiple domains (e.g. mechanical, electrical, hydraulic), while symbolic computing (MapleSim, which uses our algorithms) results in highly-optimized code for real-time simulation. We continue to develop specialized theories for contact dynamics and constitutive models.

## Control and Optimization

Starting with a dynamic model, we develop optimal controllers for automotive systems and human movements. Symbolic computing facilitates sensitivity analysis and the optimization used in our model-based controllers, which incorporate Pontryagin’s minimum principle, nonlinear model-predictive control, and other optimal control theories. Homotopy optimization has proven to be well-suited for model parameter identification from noisy or incomplete experimental data, and graph theory has been exploited in our topology optimization of mechanisms and hybrid vehicles.

## Advanced Vehicle Systems

Our multi-domain modelling and control methods are well-suited to vehicle system applications. New battery and engine models have been developed for hybrid powertrain systems; our model-based controllers reduce the fuel consumption and emissions from hybrid vehicles, and extend the range of pure electric vehicles. Our controllers are tested in real-time HIL simulations (DSpace and NI) of complete vehicle dynamics, including powertrains and new suspension models, and our contact dynamics models for off-road vehicle tire-soil interactions are experimentally validated. We have a number of Toyota vehicles (plug-in Prius, electric Rav4, RX 350) in our research fleet, which we test on our track using a $1M vehicle dynamics measurement system and in our$10M Green and Intelligent Automotive (GAIA) facility.

## Biomechanics and Sports Engineering

We are very active in the dynamic simulation and control of human movement, rehabilitation and assistive device design, and the effect of equipment design on athletic performance. Detailed models of musculoskeletal systems and foot-ground contact forces are used to predict natural human movements prior to experimental testing, and our model-based controllers effectively mimic the actions of the central nervous system. We are creating new wearable technologies based on IMUs, and our lab and field experiments make use of camera-based motion capture, an Xsens Movensuit, portable force plates and pressure mats, EMG systems, an AboutGolf simulator, hockey slapshot robot, and Photron high-speed cameras.

## Mechatronics, Mechanisms and Machinery

Our research applications go far beyond vehicles and humans; we are interested in anything that moves. We have worked on piano action mechanisms with Steinway, on MEMS actuators and sensors, and on robotic arms, walkers, and rovers with the Canadian Space Agency. We continue to work with industry partners who are tackling the dynamics and control of mechanisms and machinery, and we are always looking for a new challenge.