Optimization-based trajectory planning of the human upper body

Karim Abdel-Malek, Zan Mi, Jingzhou Yang, Kyle Nebel

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


This paper presents studies of the coordination of human upper body voluntary movement. A minimum-jerk 3D model is used to obtain the desired path in Cartesian space, which is widely used in the prediction of human reach movement. Instead of inverse kinematics, a direct optimization approach is used to predict each joint's profile (a spline curve). This optimization problem has four cost function terms: (1) Joint displacement function that evaluates displacement of each joint away from its neutral position; (2) Inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial target point to the final target point; (3) The non-smoothness function of the trajectory, which is the second derivative of the joint trajectory; (4) The non-continuity function, which consists of the amplitudes of joint angle rates at the initial and final target points, in order to emphasize smooth starting and ending conditions. This direct optimization technique can be used for potentially any number of degrees of freedom (DOF) system and it reduces the cost associated with certain inverse kinematics approaches for resolving joint profiles. This paper presents a high redundant upper-body modeling with 15 DOFs. Illustrative examples are presented and an interface is set up to visualize the results.

Original languageEnglish
Pages (from-to)683-696
Number of pages14
Issue number6
StatePublished - Nov 2006


  • B-splines
  • Biomechanics
  • Cartesian space
  • Direct optimization-based method
  • Joint space
  • Minimum jerk
  • Planning trajectory


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