Design of a Neural Controller for Walking of a 5-Link Planar Biped Robot via Optimization

Underactuation, impulsive nature of the impact with the environment, the existence of feet structure and the large number of degrees of freedom are the basic problems in control of the biped robots. Underactuation is naturally associated with dexterity [1]. For example, headstands are considered dexterous. In this case, the contact point between the body and the ground is acting as a pivot without actuation. The nature of the impact between the lower limbs of the biped walker and the environment makes the dynamic of the system to be impulsive. The foot-ground impact is one of the main difficulties one has to face in design of robust control laws for biped walkers [2]. Unlike robotic manipulators, biped robots are always free to detach from the walking surface and this leads to various types of motions [2]. Finally, the existence of many degrees of freedom in the mechanism of biped robots makes the coordination of the links difficult. According to these facts, designing practical controller for biped robots remains to be a challenging problem [3]. Also, these features make applying traditional stability margins difficult. In fully actuated biped walkers where the stance foot remains flat on the ground during single support phase, well known algorithms such as the Zero Moment Point (ZMP) principle guarantees the stability of the biped robot [4]. The ZMP is defined as the point on the ground where the net moment generated from ground reaction forces has zero moment about two axes that lie in the plane of ground. Takanishi [5], Shin [6], Hirai [7] and Dasgupta [8] have proposed methods of walking patterns synthesis based on ZMP. In this kind of stability, as long as the ZMP lies strictly inside the support polygon of the foot, then the desired trajectories are dynamically feasible. If the ZMP lies on the edge of the support polygon, then the trajectories may not be dynamically feasible. The Foot Rotation Indicator (FRI) [9] is a more general form of the ZMP. FRI is the point on the ground where the net ground reaction force would have to act to keep the foot stationary. In this kind of stability, if FRI is within the convex hull of the stance foot, the robot is possible to walk and it does not roll over the toe or the heel. This kind of walking is named as fully actuated walking. If FRI is out of the foot projection on the ground, the stance foot rotates about the toe or the heel. This is also named as underactuated walking. For bipeds with point feet [10] and