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

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.