Major research areas include:
Predictive Dynamics
Predictive dynamics: an optimization-based novel approach for human motion simulation
Structural and Multidisciplinary Optimization, 41:465-479, 2010
Predictive dynamics is a novel approach for simulating human motion. It avoids direct integration of differential-algebraic equations in order to create the resulting simulations for redundant digital human models. Instead, it formulates an optimization problem by defining appropriate performance measures and constraints to recover the real motion of the dynamic system. In the formulation, both kinematic and kinetic parameters serve as unknowns, and equations of motion are treated as equality constraints. Procedures to choose physical performance measures and appropriate constraints based on the available information about the bio-system are presented. The proposed methodology is illustrated and studied by first predicting the swinging motion of a single pendulum with externally applied torque. The pendulum can represent the motion of upper and lower extremities. This simple problem has analytical solutions and is used to gain insights for the predictive dynamics approach. In addition, a complex human walking task is simulated by using the approach, and realistic results are obtained. Such motion prediction capabilities have a wide variety of applications for industries ranging from automotive to military to clinical analysis and design.
Optimization-based motion prediction of mechanical systems: sensitivity analysis
Structural and Multidisciplinary Optimization, 37(6):551-570, 2009
In this study, we derive sensitivity equations for the problem of
optimization-based motion prediction of a mechanical system using the
inverse recursive Lagrangian formulation. The simulation and
sensitivity formulations are based on Denavit-Hartenberg transformation
matrices. External forces and moments are taken into account in the
formulation. The sensitivity information is needed in the
optimization-based simulation process. The proposed formulation is
demonstrated by calculating sensitivities for the optimal time
trajectory planning problem of a two-link manipulator. In addition,
sensitivities obtained using the proposed algorithm are compared to
those obtained using the closed-form equations of motion. The two
sensitivities match quite closely. The lifting motion of the two-link
manipulator with external loads is also optimized by using the
algorithm developed in this paper. More complex applications of the
proposed formulation to digital human motion prediction are presented
elsewhere.
Multibody System Dynamics, 28(3):199-224, 2012
A new methodology, called
hybrid predictive dynamics (HPD), is
introduced in this work to simulate human motion. HPD is defined as an
optimization-based motion prediction approach in which the joint angle
control points are unknowns in the equations of motion. Some of these
control points are bounded by the experimental data. The joint torque
and ground reaction forces are calculated by an inverse algorithm in
the optimization procedure. Therefore, the proposed method is able to
incorporate motion capture data into the formulation to predict natural
and subject-specific human motions. Hybrid predictive dynamics includes
three procedures, and each is a sub-optimization problem. First, the
motion capture data is transferred from Cartesian space into joint
space by using optimization-based inverse kinematics (IK) methodology.
Secondly, joint profiles obtained from IK are interpolated by B-spline
control points by using an error-minimization algorithm. Third,
boundaries are built on the control points to represent specific joint
profiles from experiments, and these boundaries are used to guide the
predicted human motion. To predict more accurate motion, the boundaries
can also be built on the kinetic variables if the experimental data are
available. The efficiency of the method is demonstrated by simulating a
box-lifting motion. The proposed method takes advantage of both
prediction and tracking capabilities simultaneously so that HPD has
more applications in human motion prediction, especially towards the
clinical applications.Back to top
Gait Analysis
Optimization-based dynamic human walking prediction: one step
formulation
International Journal for Numerical Methods in Engineering,
79:667-695, 2009
A new
methodology is introduced in this work to simulate normal
walking using a spatial digital human model. The proposed methodology
is based on an optimization formulation that minimizes the dynamic
effort of people during walking while considering associated physical
and kinematical constraints. Normal walking is formulated as a
symmetric and cyclic motion. Recursive Lagrangian dynamics with
analytical gradients for all the constraints and objective function are
incorporated in the optimization process. Dynamic balance of the model
is enforced by direct use of the equations of motion. In addition, the
ground reaction forces are calculated using a new algorithm that
enforces overall equilibrium of the human skeletal model. External
loads on the human body, such as backpacks, are also included in the
formulation. Simulation results with the present methodology show good
correlation with the experimental data obtained from human subjects and
the existing literature.
Optimization-based prediction of asymmetric human gait
Journal of Biomechanics, 2011, 44(4): 683-693
An optimization-based
formulation and solution method are presented to predict asymmetric
human gait for a large-scale skeletal model. Predictive dynamics
approach is used in which both the joint angles and joint torques are
treated as unknowns in the equations of motion. For the optimization
formulation, the joint angle profiles are treated as the primary
unknowns, and velocities and accelerations are calculated using them.
In numerical implementation, the joint angle profiles are discretized
using the B-spline interpolation. An algorithm is presented to
inversely calculate the joint torques and the ground reaction forces.
The sum of the joint-torques squared, called the dynamic effort, is
minimized as the human performance measure. Constraints are imposed on
the joint strengths (torques) and joint ranges of motion along with
other physical constraints. The formulation is validated by simulating
a symmetric gait and comparing the results with the experimental data.
Then asymmetric gait motion is simulated where the left and right step
lengths are different. The kinematics and kinetics results from the
simulation are presented and discussed. Predicted ground reaction
forces are explained by using the inverted pendulum model. Predicted
kinematics and kinetics have trends that are similar to those reported
in the literature. Potential practical applications of the formulation
and the solution approach are discussed.
Physics-based modeling and simulation of human walking: a review of optimization-based and other approaches
Structural and Multidisciplinary Optimization, 42:1-23, 2010
A review of human walking modeling and simulation is presented. This
review focuses on physics-based human walking simulations in the
robotics and biomechanics literature. The gait synthesis methods are
broadly divided into five categories: (i) inverted pendulum model; (ii)
passive dynamics walking; (iii) zero moment point (ZMP) methods; (iv)
optimization-based methods; and (v) control-based methods. Features of
various methods are discussed, and their advantages and disadvantages
are delineated. The modeling, formulation, and computation aspects of
each method are reviewed.
Predictive simulation of human walking
transitions using an optimization formulation
Structural and Multidisciplinary Optimization, 45:759-772, 2012
A general op
timization
formulation for transition walking prediction using 3D skeletal model
is presented. The formulation is based on a previously presented
one-step walking formulation (Int. J. Numer. Meth. Engng 2009;
79:667–695). Two basic transitions are studied: walk-to-stand and
slow-to-fast walk. The slow-to-fast transition is used to
connect slow
walk to fast walk by using a step-to-s
tep
transition formulation. In
addition, the speed effects on the walk-to-stand motion are
investigated. The joint torques and ground reaction forces (GRF) are
recovered and analyzed from the simulation. For slow-to-fast walk
transition, the predicted ground reaction forces (GRF) in step
transition is even larger than that of the fast walk. The model shows
good correlation with the experimental data for the lower extremities
except for the standing ankle profile. The optimal solution of
transition simulation is obtained in a few minutes by using predictive
dynamics method.Back to top
Manual Material Handling
Human lifting simulation using a multi-objective optimization approach
Multibody System Dynamics, 23(4):431-451, 2010.
This paper presents a
multi-objective optimization (MOO) approach to predicting dynamic
lifting for a three-dimensional, highly redundant digital human model
with 55 degrees of freedom. The optimization problem is formulated to
optimize two objective functions simultaneously - dynamic effort and
stability – subject to basic physical and kinematical constraints. The
predictive dynamics approach is used to solve for the joint angles,
torque profiles, and ground reaction forces. The weighted sum approach
of MOO is used to aggregate the two objective functions, and the Pareto
optimal set for the problem is generated by systematically varying the
weighting parameters for the objective functions. Experimental data are
used to validate the final simulation. Several examples are presented
to demonstrate the effect of the weighting parameters for the two
objective functions on the predicted box-lifting strategies. The
results show that the proposed MOO approach improves the simulation
results compared to the single objective optimization formulation.
Also, the formulation is less sensitive to the weighting coefficient
for the stability criterion.
Back to top
Crashworthiness Design
Optimal crashworthiness design of a spot-welded thin-walled hat section
Finite Elements in Analysis and Design, 42:846-855, 2006
In automotive industry,
crashworthiness design is of special
interest to ensure passengers safety and reduce vehicle costs.
Thin-wall beams are the main energy absorbing structures in frontal and
real collisions; therefore, it is important to investigate their energy
absorption and optimize their performance. For crashworthiness designs
of thin-wall sections, much attention has been put on size and shape
designs of the cross-sections, while limited study has been performed
to incorporate spot-weld modelling and their numbers as design factors
in the crashworthiness optimization process. The spacing of spot-welds
has a strong effect on crashworthiness performance, because it can
change a single complete folding length. This study focuses on the
optimal crashworthiness design of a spot-welded thin-wall hat section
subject to an axial crushing force. Based on experimental data,
appropriate models for spot-welds are used in numerical simulation. The
mass of the beam is optimized under constraints of required mean
collapse force, bending stiffness, and number of spot-welds on the
section. A two-step “RSM-Enumeration” procedure is employed to
efficiently solve this optimization problem of mixed-type variables.
Back to top