tailieunhanh - Climbing and Walking Robots part 8

Tham khảo tài liệu 'climbing and walking robots part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Simulated Regulator to Synthesize ZMP Manipulation and Foot Location for Autonomous Control of Biped Robots 203 Fig. 1 B is expressed as follows x w2 x xz ỹ w2 y yz 1 2 where Pg x y z T is the position of COM and Pz xz yz Zz T is ZMP. w is defined as 2 _ z g w2 z zz 0 . 3 where g is the acceleration of gravity and Zz is the ground level which is known. z x and y axes are aligned along the gravity the forward and the leftward directions respectively. Eq. 1 and 2 imply that COM can be controlled via manipulation of ZMP. Fig. 2. Coupled movement of ZMP and COM in the ground-kick in the double support phase. ZMP travels fast between the feet to overtake COM. The coupled movement of ZMP and COM is not simple. Let us consider a case where the robot lifts up one foot from the both-standing state for example. Note that in such situations a conventional distinction between swing foot and stance foot does not make sense any longer since neither feet are swinging. However they are obviously different from each other in terms of function. In this paper the foot to be the swing foot is called kicking foot and that to be the stance foot is called pivoting foot instead. The sequence is illustrated by Fig. 2. ZMP is required to be within the pivoting sole at the end of the phase in order to detach the kicking foot off the ground while it moves into the sole of kicking foot in the initial phase in order to accelerate COM towards the pivoting foot. Namely ZMP initially moves oppositely against the direction of the desired COM movement and overtakes COM during the motion. The fact that the biped robot is a non-minimumphase-transition system as well as the inverted pendulum underlies the requirement of such a complex manipulation of ZMP. In addition ZMP travels faster than COM between the feet in the double support phase as ZMP depends on the acceleration of the robot. Both modes of COM and ZMP movement are desired to be explicitly designed in accordance with the locations of feet. .