Major research areas include:
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
Multibody System Dynamics, 28(3):199-224, 2012A 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
Optimization-based dynamic human walking prediction: one step
International Journal for Numerical Methods in Engineering,
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, 2012A general optimization 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-step 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
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