CafkNet: GNN-Empowered Forward Kinematic Modeling for Cable-Driven Parallel Robots

TL;DR

This paper proposes a graph-based representation to model CDPRs and introduces CafkNet, a fast and general FK solving method, leveraging Graph Neural Network (GNN) to learn the topological structure and yield the real FK solutions with superior generality, high accuracy, and low time cost.

Abstract

Cable-driven parallel robots (CDPRs) have gained significant attention due to their promising advantages. When deploying CDPRs in practice, the kinematic modeling is a key question. Unlike serial robots, CDPRs have a simple inverse kinematics problem but a complex forward kinematics (FK) issue. So, the development of accurate and efficient FK solvers has been a prominent research focus in CDPR applications. By observing the topology within CDPRs, in this paper, we propose a graph-based representation to model CDPRs and introduce CafkNet, a fast and general FK solving method, leveraging Graph Neural Network (GNN) to learn the topological structure and yield the real FK solutions with superior generality, high accuracy, and low time cost. CafkNet is extensively tested on 3D and 2D CDPRs in different configurations, both in simulators and real scenarios. The results demonstrate its ability to learn CDPRs' internal topology and accurately solve the FK problem. Then, the zero-shot generalization from one configuration to another is validated. Also, the sim2real gap can be bridged by CafkNet using both simulation and real-world data. To the best of our knowledge, it is the first study that employs the GNN to solve the FK problem for CDPRs.

Figures (6)

• Figure 2: Overview of CafkNet. (a) The geometric model of a spatial CDPR with $m$ cables. (b) The proposed graph presentation for the CDPR (see sec:cdpr_graph). (c) The top-down computation scheme in each message propagation block. The cable nodes collect data from the world node and are eventually aggregated by the body node (see sec: message propagation).
• Figure 3: Configurations of CDPR in simulation and experiment scenarios. In simulation cases, we randomly generate $100$ polynomial trajectories (dashed curves) and sample $100$ poses (including position and orientation) along each trajectory.
• Figure 4: Reference trajectories and resulting trajectories solved by MLP and CafkNet under configurations (a) - (g). Top row: by MLP; Middle row: by CafkNet (one2one); Bottom row: by CafkNet (multi-task).
• Figure 5: Modeling accuracy of CafkNet working on artificial noise data. Here errors in case 1 to case 3 are generated by $\epsilon \sim \mathcal{N}(0, 5^2)$, and errors in case 4 to case 6 are generated by $\epsilon \sim \mathcal{N}(0, 10^2)$. $\mathcal{N}$ refers to the Gaussian distribution.
• Figure 6: Data sources of Sim2Real experiment for the configuration of ExpC4. (i) Simulated data. In the simulator, there are $100$ random trajectories and $100$ samplings per trajectory. (ii) Clean data. In the simulator, we have devised a target trajectory (dashed curve) to control the real CDPR to execute it. Here $1000$ samplings are generated. (iii) Noise data. In the real setup, the end-effector of CDPR follows the target trajectory. During the experiment, a total of 1103 data are collected. Above all, each data composes the end-effector pose ($x,y,\theta$) and the corresponding length of $4$ cables.