A mathematical analysis of the minimum variance model of human-like reaching movements

The paper deals with modeling of human-like reaching movements using a probabilistic minimum variance model. A continuous formulation of the minimum variance model is developed and analyzed. The model features a parameter, having the meaning of the post-movement time period, whose assignment in a systematic way is not evident. To facilitate the situation and avoid the explicit specification of this parameter, the limiting case of the post-movement period tending to infinity is analyzed for several classes of the control plant. A connection between this limiting model and the conventional minimum control effort model is also established.

[1]  Abba B. Gumel,et al.  Mathematical analysis of the role of repeated exposure on malaria transmission dynamics , 2008 .

[2]  T. Flash,et al.  The coordination of arm movements: an experimentally confirmed mathematical model , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[3]  Yiannis Demiris,et al.  Optimal robot arm control using the minimum variance model , 2005, J. Field Robotics.

[4]  Zhiwei Luo,et al.  Reaching Movements in Dynamic Environments: How Do We Move Flexible Objects? , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[5]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[6]  A. Wiegner,et al.  Kinematic models and human elbow flexion movements: Quantitative analysis , 2004, Experimental Brain Research.

[7]  Yiannis Demiris,et al.  Object Grasping using the Minimum Variance Model , 2006, Biological Cybernetics.

[8]  Zhiwei Luo,et al.  On the dynamic version of the minimum hand jerk criterion , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[9]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[10]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[11]  J. F. Soechting,et al.  Invariant characteristics of a pointing movement in man , 1981, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  C. Harris.  On the optimal control of behaviour: a stochastic perspective , 1998, Journal of Neuroscience Methods.

[13]  Suguru Arimoto,et al.  Natural resolution of ill-posedness of inverse kinematics for redundant robots: a challenge to Bernstein's degrees-of-freedom problem , 2005, Adv. Robotics.

[14]  P. Morasso.  Spatial control of arm movements , 2004, Experimental Brain Research.

[15]  Ning Qian,et al.  Different Predictions by the Minimum Variance and Minimum Torque-Change Models on the Skewness of Movement Velocity Profiles , 2004, Neural Computation.

[16]  Yoshiyuki Tanaka,et al.  Bio-mimetic trajectory generation of robots via artificial potential field with time base generator , 2002, IEEE Trans. Syst. Man Cybern. Part C.

[17]  R. Happee,et al.  Time optimality in the control of human movements , 1992, Biological Cybernetics.

[18]  Neville Hogan,et al.  Optimization principles in motor control , 1998 .

[19]  H. Nagasaki.  Asymmetric velocity and acceleration profiles of human arm movements , 2004, Experimental Brain Research.

[20]  Jack M. Winters,et al.  Analysis of Fundamental Human Movement Patterns Through the Use of In-Depth Antagonistic Muscle Models , 1985, IEEE Transactions on Biomedical Engineering.

[21]  Daniel M. Wolpert,et al.  Making smooth moves , 2022 .

[22]  Zhiwei Luo,et al.  Optimal trajectory formation of constrained human arm reaching movements , 2004, Biological Cybernetics.

[23]  D. J. Hanson,et al.  Book Reviews : Harold Fallding, The Sociological Task : A Concise Introduction to the Main Issues in Sociological Theory and Method. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1958 , 1970 .

[24]  M. Kawato,et al.  Formation and control of optimal trajectory in human multijoint arm movement , 1989, Biological Cybernetics.

[25]  Winston Garira,et al.  Mathematical analysis of a model for HIV-malaria co-infection. , 2009, Mathematical biosciences and engineering : MBE.