Abstract
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.
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Bottaso, C.L., Prilutsky, B.I., Croce, A., Imberti, E., Sartirana, S.: A numerical procedure for inferring from experimental data the optimization cost functions using a multi-body model of the neuro-musculoskeletal system. Multibody Syst. Dyn. 16, 123–154 (2006)
Choi, J., Armstrong, T.J.: 3-D Dimensional kinematic model for predicting hand posture during certain gripping tasks. In: ASB 29th Annual Meeting (2005)
Craig, J.J.: Introduction to Robotics: Mechanics and Control, 3rd edn. (2006)
Das, B., Behara, D.N.: Three-dimensional workspace for industrial workstations. Human Factors 40(4), 633–646 (1998)
Das, I., Dennis, J.: Normal-boundary intersection: an alternate method for generating pareto optimal points in multicriteria optimization problems, NASA Contract No. NASI-19480 (November 1996)
Dong, Z., Xu, J., Zou, N., Chai, C.: Posture prediction based on orthogonal interactive genetic algorithm. In: Fourth International Conference on Natural Computation, vol. 1, pp. 336–340 (2008)
Dysart, M.J., Woldstad, J.C.: Posture prediction for static sagittal-plane lifting. Journal of Biomechanics 29(10), 1393–1397 (1996)
Faraway, J.J., Zhang, X.D., Chaffin, D.B.: Rectifying postures reconstructed from joint angles to meet constraints. Journal of Biomechanics 32, 733–736 (1999)
Gill, P., Murray, W., Saunders, A.: SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM Journal of Optimization 12(4), 979–1006 (2002)
Gragg, J., Yang, J., Boothby, R.: Posture reconstruction method for mapping joint angles from motion capture experiment to simulation models. In: HCII 2011, Hilton Orlando Bonnet Creek, Orlando, Florida, USA, July 9-14 (2011)
Halvorsen, K., Lesser, M., Lindberg, A.: A new method for estimating the axis of rotation and the center of rotation. Journal of Biomechanics 32, 1221–1227 (1999)
Howard, B., Yang, J., Gragg, J.: Toward a new digital pregnant woman model and posture prediction. In: 1st International Conference on Applied Digital Human Modelling, Miami, Florida, July 17-20 (2010)
Jung, E.S., Park, S.: Prediction of human reach posture using a neural network for ergonomic man models. Computers & Industrial Engineering 27(1-4), 369–372 (1994)
Jung, E.S., Choe, J.: Human reach posture prediction based on psychophysical discomfort. International Journal of Industrial Ergonomics 18, 173–179 (1996)
Khan, S.U., Ardil, C.: A weighted sum technique for the joint optimization of performance and power consumption in data centers. International Journal of Electrical, Computer, and Systems Engineering 3, 1 (2009)
Kim, I.Y., Weck, O.L.: Adaptive weighted sum method for multiobjective optimization. In: AIAA, 2004–4322 (2004)
Kim, I.Y., Weck, O.L.: Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct. Multidisc. Optim. 29, 149–158 (2005)
Ma, L., Wei, Z., Chablat, D., Bennis, F., Guillaume, F.: Multi-objective optimization method for posture prediction and analysis with consideration of fatigue effect and its application case. Computers & Industrial Engineering 57(4), 1235–1246 (2009)
Messac, A., Mattson, C.A.: Generating well-distributed sets of pareto points for engineering design using physical programming. Optimization and Engineering 3, 431–450 (2002)
Mi, Z., Yang, J., Abdel-Malek, K.: Real-time inverse kinematics for humans. In: Proceedings of 2002 ASME Design Engineering Technical Conferences, Montreal, Canada, September 29-October 2 (2002)
Mi, Z., Yang, J., Abdel-Malek, K.: Optimization-based posture prediction for human upper body. Robotica 27(4), 607–620 (2009)
Miller, C., Mulavara, A., Bloomberg, J.: A quasi-static method for determining the characteristic of motion capture camera system in a ‘split-volume’ configuration. Gait & Posture 16(3), 283–287 (2002)
Robert, J.J., Michele, O., Gordon, L.H.: Validation of the Vicon 460 motion capture systemTM for whole-body vibration acceleration determination. In: ISB XXth Congress-ASB 29th Annual Meeting, Cleveland, Ohio, July 31-August 5 (2005)
Saaty, T.L.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 57–68 (1977)
Saaty, T.L., Vargas, L.G.: The Logic of Priorities: Applications of the Analytic Hierarchy Process in Business, Energy, Health, & Transportation. RWS Publications, Pittsburgh (1991)
Tolani, D., Goswami, A., Badler, N.: Real-time inverse kinematics techniques for anthropomorphic limbs. Graphical Models 62, 353–388 (2000)
Wang, X.: Behavior-based inverse kinematics algorithm to predict arm prehension postures for computer-aided ergonomic evaluation. Journal of Biomechanics 32(5), 453–460 (1999)
Yang, J., Marler, R.T., Kim, H., Arora, J., Abdel-Malek, K.: Multi-objective optimization for upper body posture prediction. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, USA, August 30-September 1 (2004)
Yang, J., Abdel-Malek, K., Marler, T., Kim, J.: Real-time optimal reach posture prediction in a new interactive virtual environment. Journal of Computer Science and Technology 21(2), 189–198 (2006)
Yang, J., Kim, J.H., Abdel-Malek, K., Marler, T., Beck, S., Kopp, G.R.: A new digital human environment and assessment of vehicle interior design. Computer-Aided Design 39, 548–558 (2007)
Yang, J., Marler, T., Rahmatalla, S.: Multi-objective optimization-based kinematic posture prediction: development and validation. Robotics (2010) (in press)
Zeleny, M.: Compromise Programming in Multiple Criteria Decision Making, pp. 262–301. University of South Carolina Press, Columbia (1973)
Zhang, J., Fan, Y., Jia, D., Wu, Y.: Kinematic simulation of a parallel NC machine tool in the manufacturing process. Front. Mech. Eng. China 2, 173–176 (2006)
Zhang, K.S., Li, W.J., Song, W.P.: Bi-level adaptive weighted sum method for multidisciplinary multi-objective optimization. In: AIAA 2008-908 (2008)
Zhang, W.H., Yang, H.C.: A study of the weighting method for a certain type of multicriteria optimization problem. Computers and Structures 79, 2741–2749 (2001a)
Zhang, W.H., Gao, T.: A min–max method with adaptive weightings for uniformly spaced Pareto optimum points. Computers and Structures 84, 1760–1769 (2006)
Zhang, W.H., Domaszewski, M., Fleury, C.: An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization. International Journal for Numerical Methods in Engineering 52, 889–902 (2001b)
Zou, Q.L., Zhang, Q.H., Yang, J.: Determining weights of joint displacement function in direct optimization-based posture prediction–A pilot Study. In: The 3rd International Conference on Applied Human Factors and Ergonomics, Miami, FL (July 2010)
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Zou, Q., Zhang, Q., Yang, J.(., Boothby, R., Gragg, J., Cloutier, A. (2011). An Alternative Formulation for Determining Weights of Joint Displacement Objective Function in Seated Posture Prediction. In: Duffy, V.G. (eds) Digital Human Modeling. ICDHM 2011. Lecture Notes in Computer Science, vol 6777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21799-9_27
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