Determining weights of joint displacement objective function for standing reach tasks

This paper presents an inverse optimization approach to determine the weights for the joint displacement function in standing reach tasks. 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 sets of joint angles (the design variables and the realistic standing reach posture). Constraints include (1) normalized weights within limits; (2) an inner optimization problem to solve for joint angles (predicted standing reach posture). Additional constraints such as weight linear equality constraints, obtained through observations, are also implemented in the formulation to test the method. A 52 degree-of-freedom (DOF) human whole body model is used to study the formulation and visualize the prediction. An in-house motion capture system is used to obtain the realistic standing reach posture. Total 12 subjects (three subjects for each percentiles in stature of 5th percentile female, 50th percentile female, 50th percentile male and 95th percentile male) are selected to run the experiment. The set of weights for the general standing reach tasks is obtained by averaging all weights for all subjects and all tasks. Based on obtained set of weights, the predicted standing reach postures have good correlation with the experimental results. The presented formulation can be used to determine the weights of cost function within any multi-objective optimization (MOO) problems such as any types of posture prediction and motion prediction.