The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are sufficient conditions to ensure rolling. The differential geodesic equations, when modified, can ensure proper disturbance rejection in case the system of interacting bodies is perturbed from the desired curve. A corollary states that geodesic curves are generated on the surface if rolling constraints are satisfied. Simulations in the context of in-hand manipulations of the objects are used as examples.

中文翻译：

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关于合成基于测地线的接触曲线的注意事项

本文着重于合成最佳接触曲线，以确保相对运动中两个物体之间的滚动约束。我们表明，在两个接触面上生成的基于测地线的接触曲线是确保滚动的充分条件。修改后的微分测地线方程可以确保适当的干扰抑制，以防相互作用的物体系统受到所需曲线的干扰。推论表明，如果满足滚动约束，则在表面上会生成测地曲线。在对象的手动操作的上下文中的仿真被用作示例。