Kuo A D
Department of Mechanical Engineering & Applied Mechanics, University of Michigan, Ann Arbor 48109, USA.
J Biomech Eng. 1998 Feb;120(1):148-59. doi: 10.1115/1.2834295.
A least-squares approach to computing inverse dynamics is proposed. The method utilizes equations of motion for a multi-segment body, incorporating terms for ground reaction forces and torques. The resulting system is overdetermined at each point in time, because kinematic and force measurements outnumber unknown torques, and may be solved using weighted least squares to yield estimates of the joint torques and joint angular accelerations that best match measured data. An error analysis makes it possible to predict error magnitudes for both conventional and least-squares methods. A modification of the method also makes it possible to reject constant biases such as those arising from misalignment of force plate and kinematic measurement reference frames. A benchmark case is presented, which demonstrates reductions in joint torque errors on the order of 30 percent compared to the conventional Newton-Euler method, for a wide range of noise levels on measured data. The advantages over the Newton-Euler method include making best use of all available measurements, ability to function when less than a full complement of ground reaction forces is measured, suppression of residual torques acting on the top-most body segment, and the rejection of constant biases in data.
提出了一种用于计算逆动力学的最小二乘法。该方法利用多节段身体的运动方程，纳入了地面反作用力和扭矩项。所得系统在每个时间点都是超定的，因为运动学和力的测量数量超过了未知扭矩的数量，可以使用加权最小二乘法求解，以得出最符合测量数据的关节扭矩和关节角加速度估计值。误差分析使得预测传统方法和最小二乘法的误差大小成为可能。该方法的一种改进还使得能够消除诸如由力板和运动学测量参考系未对准引起的恒定偏差。给出了一个基准案例，该案例表明，与传统的牛顿 - 欧拉方法相比，对于测量数据上的各种噪声水平，关节扭矩误差降低了约30%。相对于牛顿 - 欧拉方法的优势包括充分利用所有可用测量值、在测量的地面反作用力不足时仍能起作用、抑制作用于最上面身体节段的残余扭矩以及消除数据中的恒定偏差。
