Robot Models for Alpine Skiing and Computer Simulation

我们已经开发了各种类型的高山滑雪机器人，以期澄清滑雪者的运动的基本要素，看起来复杂的转弯。这些滑雪机器人具有简单的结构，它们的运动仅限于少数关节的旋转。然而，这些滑雪机器人可以连续地执行重复转弯，并表现出人类滑雪者执行的滑雪转弯的基本特征。因此，我们把这些机器人作为人类滑雪运动员的模型，以定量分析滑雪转弯的机理。我们假设简单的数学模型的高山滑雪机器人，并推导出模型的运动方程。滑雪板与雪面之间的相互作用被假定为摩擦力。在实际条件下，我们数值求解运动方程。解决方案被放入计算机图形显示模型的转向行为。这些计算机模拟表明，高山滑雪机器人的转向行为的基本特征，也是那些人类滑雪者被很好地再现。从这些结果中发现，滑雪运动员的动作最重要的元素是髋关节绕股骨轴旋转，并建议滑雪运动员的适当姿势，以稳定的滑雪转弯。

We have developed various kinds of Alpine skiing robot with a view to clarifying the basic elements of skier' s movements which look complicated during turns. These skiing robots have simple structure and their movements are restricted to the rotations of a few number of their joints only. However, these skiing robots can perform repeated turns continuously and exhibit basic features of the skiing turns performed by human skiers. We therefore take these robots as models of human skier, in order to analyze the mechanism of skiing turn quantitatively. We assume simple mathematical models for the Alpine skiing robots and derive the equations of motion of the models. The interaction between skis and snow surface is assumed to be frictional force. Under realistic conditions, we solve the equations of motion numerically. The solutions are put into computer graphics showing the turning behavior of the model. These computer simulations show that the essential features of turning behavior of the Alpine skiing robots and also those of the human skier are well reproduced. From these results, it is found that the most important element of skier' s movements is the rotation of the hip joints around the femur axes, and an appropriate posture of skier to stable skiing turns is suggested.