Human posture prediction can often be formulated as a nonlinear multiobjective optimization (MOO) problem. The joint displacement function is considered as a benchmark of human performance measures. When the joint displacement function is used as the objective function, posture prediction is a MOO problem. The weighted-sum method is commonly used to find a Pareto solution of this MOO problem. Within the joint displacement function, the relative value of the weights associated with each joint represents the relative importance of that joint. Usually, weights are determined by trial and error approaches. This paper presents a systematic approach via an inverse optimization approach to determine the weights for the joint displacement function in posture prediction. This inverse optimization problem can be formulated as a bi-level optimization problem. The design variables are joint angles and weights. The cost function is the summation of the differences between two set of joint angles (the design variables and the realistic posture). Constraints include (1) normalized weights within limits and (2) an inner optimization problem to solve for joint angles (predicted posture). Additional constraints such as weight limits and weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 24 degree of freedom human upper body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the realistic posture. Four different percentiles of subjects are selected to run the experiment. The set of weights for the general seated posture prediction is obtained by averaging all weights for all subjects and all tasks. On the basis of obtained set of weights, the predicted postures match the experimental results well.
The human posture prediction model is one of the most important and fundamental components in digital human models. The direct optimization-based method has recently gained more attention due to its ability to give greater insights, compared to other approaches, as how and why humans assume a certain pose. However, one longstanding problem of this method is how to determine the cost function weights in the optimization formulation. This paper presents an alternative formulation based on our previous inverse optimization approach. The cost function contains two components. The first is the weighted summation of the difference between experimental joint angles and neutral posture, and the second is the weighted summation of the difference between predicted joint angles and the neutral posture. The final objective function is then the difference of these two components. Constraints include (1) normalized weights within limits; (2) an inner optimization problem to solve for the joint angles, where joint displacement is the objective function; (3) the end-effector reaches the target point; and (4) the joint angles are within their limits. Furthermore, weight limits and linear weight constraints determined through observation are implemented. A 24 degree of freedom (DOF) human upper body model is used to study the formulation. An in-house motion capture system is used to obtain the realistic posture. Four different percentiles of subjects are selected and a total of 18 target points are designed for this experiment. The results show that using the new objective function in this alternative formulation can greatly improve the accuracy of the predicted posture.
This paper presents an optimization-based dynamic simulation for pregnant women pseudo standing, forward falling, and pulling tasks. Based on anatomy of pregnant women a digital pregnant woman model is developed. The model has 55 degrees of freedom (DOFs) including 6 global DOFs and 49 body DOFs. Recursive dynamic algorithm is used to formulate the equations of motion. Human motion can be formulated as a non-linear optimization problem. Control points of B-spline curves that represent joint angle profiles are design variables. The joint angles, angular velocities and angular accelerations, will be obtained from the control points. The summation of all joint actuator torque square acts as the objective function. Besides some common constraints, different constraints are adopted for standing, falling, and pulling, respectively. Three cases, non-pregnancy, 6-month, and 9-month pregnancy, are investigated. For the pulling task, 2N, 100N or 200N external load is applied as the pulling force. Determinant joints (hip, knee and ankle) are plotted to analyze the simulation results. The simulation results show the effects of pregnancy on human movement kinematics and dynamics. The average computational time for each case is close to 3.5 minutes in a Dell computer with 3.25 GB of RAM and 3.16 GHz.
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