Biped Locomotion

The motion of living organisms by means of legs, especially the locomotion of bipeds, has always been a challenging problem to scientists of different vocations: biologists, physiologists, medicine specialists, mathematicians, and engineers. In spite of their efforts, however, this problem has not been solved yet in a satisfactory way.

The active spatial mechanism for realization of the artificial anthropomorphic gait belongs to the class of complex kinematic chains. During the single-support gait phase, the mechanism is a complex open kinematic chain, while in the double-support phase one of the chains becomes closed. This chapter is devoted to the description of a computer procedure for forming the dynamic equations of motion of such mechanism, comprising both the open and closed complex kinematic chains. The procedure is based on the methods by which the computer forms the mathematical models for simple open kinematic chains. These methods were described in detail in the previous books of this series [1–3].

In this chapter we shall present the theoretical foundations of control synthesis for two-leg locomotion systems. Because of the presence of unpowered degrees of freedom (d.o.f.), the most serious problem which has to be solved is the overall system stability. This is the reason why the control synthesis at two stages has been adopted. At the first stage, the stage of nominal regimes, such control has to be synthesized to ensure the system’s motion in the absence of any disturbance along the exact nominal trajectories calculated in advance. It should be derived in such a way to satisfy the conditions of both the desired gait type and overall system equilibrium. At the second stage, the stage of perturbed regimes, only deviation of the actual state vector from its nominal value is considered, and additional control is applied to force the system state to its nominal. However, the movement thus realized, can induce an additional inertial force which, on the other hand, can produce rotation, of the whole system around the foot edge. The movement should not wake the situation worse, by producing some additional inertial forces. As the nominal system motion is synthesized under the condition of the overall system equilibrium, the best way to realize the system’s return from a disturbed to its nominal regime is to prevent the excursion of the system state out of a certain finite region.

Locomotion activity, and especially the human gait, belongs to a class of highly automated motion. Bernstein was the first who noticed this fact [1], It is known that man has at the disposal for his complete sceletal (locomotion-manipulation) activity several hundreds of muscles which form over three hundred and fifty equivalent d.o.f. In view of such a high number of biological actuators through which man exercises his motor activity the imitation of this activity seems to be a hopelessly dificult task. To grasp the essence of the gait mechanism control and of other skeletal activity is also a task of extreme complexity if one has in mind the detailed insight into the multilevel structure of the extremely complex and perfect control of the human gait, i.e. of human locomotion and manipulation activity.