Dynamics Model of a Biped Walking Machine : A Method of Joint Accelerations Calculation using Newton-Euler Equations

A method of calculating joint accelerations of a biped walking machine is proposed using Newton-Euler equations. The method transcribes all the phases in walking into the corresponding conditions on a linear equation with respect to the trunk, thus eliminating the conventional model change. The force and torque vectors from link i-1 to link i, the linear/angular acceleration vectors of link i-1, and the i-1 th joint acceleration are expressed recursively in linear terms with respect to the force and torque vectors from the ground to the foot (link 0) and the linear/angular acceleration vectors of the foot. The unknown vectors are solved by a 26×26 linear equation with respect to the trunk and feet conditions. Then the joint accelerations can be solved using the unknowns. Numerical experiment applied to a 4-degrees-of-freedom (dof) stilt machine solved the joint accelerations using this method. The condition number of the linear equation is 2×104, thus double precision QR decomposition is employed.