During planar motion, contact surfaces exhibit a coupling between tangential and rotational friction forces. This article proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended state models are proposed, and the elastoplastic model is extended for multidimensional friction. Subsequently, we derive a reduced planar friction model coupled with a precalculated limit surface, which offers the reduced computational cost. The limit surface approximation through an ellipsoid is discussed. The properties of the planar friction models are assessed in various simulations, demonstrating that the reduced planar friction model achieves comparable performance to the distributed model while exhibiting$\sim\! 80$times the lower computational cost.

In this paper, we propose a new framework for solving cable-routing problems with a dual-arm robot, where the objective is to clip a Deformable Linear Object (DLO) into several arbitrarily placed fixtures. The core of the framework is a task-space planner, which builds a roadmap from predefined tasks and employs a replanning strategy based on a genetic algorithm, if problems occur. The manipulation tasks are executed with either individual or coordinated control of the arms. Moreover, hierarchical quadratic programming is used to solve the inverse differential kinematics together with extra feasibility objectives. A vision system first identifies the desired fixture route and structure preserved registration estimates the state of the DLO in real-time. The framework is tested on real-world experiments with a YuMi robot, demonstrating a 90% success rate for 3 fixture problems.