An inverse optimization approach for determining weights of joint displacement objective function for upper body kinematic posture prediction

Abstract

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.

Development Of A Bi-Criterion Objective Function For Analytical Inverse Kinematic Methods

“…Therefore, in this research, joint displacement is calculated from initial posture. Equation ( 6) shows a commonly-used formulation of the joint displacement function [17].     where, q i i is the initial value of i th joint angle (unit: degree or rad), ω i is the joint weight of the i th joint angle (with no unit).…”

“…Zou et al determined the weights in joint displacement function by means of inverse optimization [17]. Their joint displacement function is validated in whole-body reaching tasks and predicts reasonably accurate body postures [17].…”

“…Zou et al determined the weights in joint displacement function by means of inverse optimization [17]. Their joint displacement function is validated in whole-body reaching tasks and predicts reasonably accurate body postures [17]. However, when the torso is fixed, its accuracy turns out to be low, which exhibits that the joint displacement function is not feasible for all types of reaching tasks.…”

“…Therefore, in this research, selected single objective functions (the joint displacement function and joint discomfort function) were initially combined with AIK method, respectively. Then, we examined the accuracy of the body postures, predicted by the joint displacement function [17] and the joint discomfort function [15]. Then, we comprehensively combined the selected single objective functions together, proposing a new bi-criterion objective function.…”

Posture prediction and optimization for a manual assembly operation involving lifting of weights

“…and at the upper/lower limits of each joint are specified in Table 1. QU and QL are defined mathematically and discomfort function are derived [25,26].…”