Stereotypic human movements observed in basic experimental tasks have been studied from the viewpoint of optimality with respect to some criteria. Recently, such framework is expected to be applied to understanding skilled realistic movements. This paper deals with a gymnastic maneuver on the high bar, called the kip movement, as a difficult goal-directed task under a nonholonomic constraint. The movements in such system are highly restricted by the constraint; however, it is difficult to imagine that to what extent redundancy remains for achieving the task. Thus, we study on the redundancy underlying the kip movement in this paper. To this end, a simple dynamical model of the kip movement is constructed, where the time histories of angles of actuated joints are parameterized by fifth spline functions. The movement of this model is confirmed to be approximately consistent with a measured movement of an expert gymnast. We propose a systematic method to numerically calculate a set of the spline parameters that achieve the task. A part of the redundancy underlying the kip movement is concretely illustrated. Moreover, we discuss what kind of criteria could be satisfied in the kip movement of expert gymnasts by using the set.

This paper concerns a swing-up control problem for a three-link gymnastic planar robot in a vertical plane with its first joint being passive (unactuated) and the rest being active (actuated). The objectives of this paper are to: (1) design a controller under which the robot can be brought into any arbitrarily small neighborhood of the upright equilibrium point, where all three links of the robot remain in their upright positions; and (2) attain a global analysis of the motion of the robot under the controller. To tailor the energy-based control approach to achieve the aforementioned objectives, first, this paper considers the links 2 and 3 as a virtually composite link, and proposes a coordinate transformation of the angles of active joints. Second, this paper constructs a novel Lyapunov function based on the transformation, and devises an energy-based swing-up controller. Third, this paper carries out a global analysis of the motion of the robot under the controller, and establishes some conditions on control parameters for achieving the swing-up control objective. To validate the theoretical results obtained, this paper provides simulation results for a three-link robot with its mechanical parameters being obtained from a human gymnast.

Studies the swing up control for the Acrobot, i.e., to move the Acrobot from its stable downward position to its unstable inverted position and balance it about the vertical. The combination of the partial linearization control for the swing up phase proposed by Spong (1995) and the robust control for the capture and balance phase is utilized in this paper. The key idea is first to treat the speed of the second link when it rotates across the vertical as an uncertainty, and then to design a robust controller based on the quadratic stabilization method to cope with such uncertainty. It is shown that that the robust controller is generally superior to the LQR controller in capturing and balancing the Acrobot, and the difficulty of tuning the gains in the swing up phase can be ameliorated.