Rolling a dynamic object with a planar soft-fingertip robot arm

Force-position control through one or multiple robots, or fingers, typically assumes a rigid endpoint without rolling nor slipping. However, there are some interesting tasks where rolling is involved, such as turning a knob (object is pivoting at a fixed rotational axis) or rolling a wheel (object rotational axis is moving). In such a case, rigid endpoint force control becomes very difficult if not impossible, even for us humans. This stems from two facts, firstly, infinitesimally small rigid point does not yield a tangent force, therefore it is very difficult to control it indirectly; and secondly, the pair robot-object stands for a highly non-linear constrained underactuated dynamical systems. In this paper, we aim at exploring rolling of a rigid dynamic circular object with hemispherical deformable fingertip, then with area, not point, contact. The dynamic model and a control scheme are presented inspired in previous works, but regulation of normal and tangential forces, as well as position and orientation of the object are synthesized. In particular, tangential force control proves instrumental to regulate posture, and displacement of the object with a simple transpose Jacobian Cartesian PDF+g control. Regulation of rolling angle and displacement with stable normal and tangential forces are obtained without force sensing, neither any model of the deformation nor any dynamic parameter of the object. To entertain these control objectives, a redundant configuration is required so as to yield local regulation, based on the stability-in-the-manifold criteria, whose dimension is greater than the operational space. Illustrative simulations are discussed that provide insight into the closed-loop numerical performance, and finally, remarks on the structure and potential applications are addressed.