Modeling, Identification and Control, Vol. 31, No. 3, 2011, pp. 91–101, ISSN 1890–1328 Modeling of Human Arm Energy Expenditure for Predicting Energy Optimal Trajectories L. Zhou 1 S. Bai 1 M. R. Hansen 2 J. Rasmussen 1 1 Department of Mechanical and Manufacturing Engineering, Aalborg University, 9220 Aalborg, Denmark. E-mail: {lzh,shb,jr}@m-tech.aau.dk 2 Department of Engineering, University of Agder, Grimstad, Norway. E-mail: michael.r.hansen@uia.no Abstract Human arm motion can inspire the trajectory planning of anthropomorphic robotic arms to achieve energy- efficient movements. An approach for predicting metabolic cost in the planar human arm motion by means of the biomechanical simulation is proposed in this work. Two biomechanical models, including an analytical model and a musculoskeletal model, are developed to implement the proposed approach. The analytical model is developed by modifying a human muscle expenditure model, in which the muscles are grouped as torque providers for computation efficiency. In the musculoskeletal model, the predication of metabolic cost is conducted on the basis of individual muscles. With the proposed approach, metabolic costs for parameterized target-reaching arm motions are calculated and utilized to identify optimal arm trajectories. Keywords: metabolic cost; human arm motion; musculoskeletal model; biomechanics 1 Introduction A human arm has seven dof (degrees-of-freedom) upon basic definition, three in the shoulder, two in the elbow, and two in the wrist. The redundancy in the arm dof implies infinite possible trajectories for a given move- ment task. For instance, when we pick up a bottle of water, there are a great number of trajectories that the arm can follow. With the hand located at a fixed point, the arm can also have different orientations. The mechanism behind the selection of the pre- dictable trajectory has been the subject of study over the years. The kinematic analysis (Flash and Hogan, 1985; Atkeson and Hollerbach, 1985) revealed some in- teresting kinematic features of arm motions, but could not explain the planning mechanism for the activa- tion of the individual muscle. One effective approach to study the planning mechanism is to examine the mechanical and physiological properties of a muscle, and to investigate the behaviour of individual mus- cles in human arm trajectories (Kashima et al., 2002; Fagg et al., 2002; Georgopoulos et al., 1986). Exper- imental data on multi-joint human arm trajectories obtained from restricted horizontal planar movements have shown that human point-to-point arm motion trajectories have bell-shaped velocity profiles (Abend et al., 1982; Morasso, 1981). Efforts were made to explain the observed trajectories as solutions to op- timization problems. Optimization criteria have been proposed including minimum jerk theory (Flash and Hogan, 1985), minimum travel cost theory (Rosen- baum et al., 1995), minimum isometric torque deriva- tive (Kashima and Isurugi, 1998), and averaged specific power (Secco et al., 2005). The criteria used in the opti- mal trajectory study include also the minimum energy cost hypothesis for human arm trajectories presented and tested by Alexander (1997), among others. This paper reports our study of human arm in pla- nar motion. Our study focuses on the metabolic energy costs in human arm motions. Two human arm models, doi:10.4173/mic.2011.3.1 c  2011 Norwegian Society of Automatic Control