衝撃時における二足歩行機械の順動力学モデルの構築 : 関節角速度の増分の一計算法

概要

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A method of calculating the increment of the joint angle velocity vector at the impact, Δq, which is substantial to the forward dynamics is proposed using Newton-Euler equations. First, assuming that (1) a landing leg does not bounce, (2) the force and the torque vectors from the ground are delta functions of time t, and (3) the joint torque vector is piecewise continuous in t, we obtain the increment of the joint angle velocity of the joint i, Δq_i, and the increments of the linear and angular velocities of the frame attached to the link i, Δv_i and Δw_i, as homogeneous linear equations with respect to the increments of the linear and angular velocities of the frame attached to the foot link 0, Δv_0 and Δw_0, and the impulse force and torque from the ground to the foot link, δ_f and δ_n. Next,14 homogeneous linear equations in (Δw^s_0, Δv^s_0, δ^s_f, δ^s_n)_<s=r,l> (r : right, l : left) are derived recursively using the above equations from the foot link to the trunk link. Then, imposing the feet conditions to the linear system, we obtain all the unknowns including Δq. A numerical experiment of the method applied to a 4-degree-of-freedom (dof) biped walking machine with stilt foot links shows (1) all the unknowns including Δq are obtained, and (2) the 14×12 system of linear equations to be solved in the method is of full rank in almost all the cases.
一般社団法人日本機械学会の論文
1991-10-25