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Using the generalized inverted pendulum to generate less energy-consuming trajectories for humanoid walking

Omran S., Sakka S., Aoustin Y.

Archive of Mechanical Engineering

2016

Vol. LXIII, nr 2

245--262

This paper proposes an analysis of the effect of vertical position of the pivot point of the inverted pendulum during humanoid walking. We introduce a new feature of the inverted pendulum by taking a pivot point under the ground level allowing a natural trajectory for the center of pressure (CoP), like in human walking. The influence of the vertical position of the pivot point on energy consumption is analyzed here. The evaluation of a 3D Walking gait is based on the energy consumption. A sthenic criterion is used to depict this evaluation. A consequent reduction of joint torques is shown with a pivot point under the ground.

W pracy przedstawiono propozycję analizy efektów zmiany pozycji pionowej punktu obrotu wahadła odwróconego użytego do modelowania chodu robota człekopodobnego. Wprowadzona modyfikacja wahadła polega na przesunięciu punktu obrotu poniżej poziomu gruntu, co umożliwia uzyskanie naturalnej trajektorii środka nacisku (CoP), jak w chodzie człowieka. Przeanalizowano wpływ pozycji pionowej punktu obrotu na zużycie energii. Dokonano oceny chodu w trzech wymiarach, bazując na konsumpcji energii. W ocenie zastosowano także kryterium minimum kwadratów momentów obrotowych (sthenic criterion). Uzyskana tą drogą redukcja momentów obrotowych stawów jest widoczna, gdy punkt obrotu znajduje się poniżej poziomu gruntu.

Feed-forward torques and reference trajectory for an arm with flexible joints

Aoustin Y., Formal'sky A.

Archives of Control Sciences

2002

Vol. 12, no. 1/2

125-149

We propose a design method of the feed-forward torques and the reference trajectory for an arm with flexible joints and unknown stiffiness coefficients. The bounds on the control torque are included explicitly. The designed commanded feed-forward torques and the corresponding reference trajectory are close to be time-optimal. The control law for each drive torque is composed with the commanded feed-forward torque and linear angular position and velocity feedback. The torques and the trajectory are used as input signals of PD-controllers. In a case of one-link flexible arm it is proved that so-called 'fluent' control torque enables to reach the desired motion with a small error and without large vibrations in the flexible joint. Designed fluent commanded feed-forward torque is successfully implemented in numerical experiments. The stiffness coefficient is assumed to be unknown so the mathematical model of the flexible arm is not known exactly. In two-link flexible arm the stiffness coefficients are also assumed unknown. Due to discontinuities of the optimal control functions and not acceptable jumps in the optimal control torques a 'trapezoidal' fluent control technique is proposed. Numerical experiments show that the designed control is close to time-opitimal. The approach presented in the paper can be extended to systems with more links and can take the gravity into consideration. however, in this case a time-optimal or a quasi-time-optimal control for the associated rigid system have to be designed.