Source-linked AI summary
Dynamic Modeling of a Welding Torch Umbilical and Its Impact on Robot Dynamics
Nicolas Gautier, Yves Guillermit, Mathieu Porez, Fabien Rousset, Damien Chablat
TL;DR
The paper addresses how external welding umbilicals affect robot dynamics, particularly for lightweight and collaborative robots. It models the umbilical as a constrained passive-joint multibody system with elastic and dissipative effects, reduces the dynamics through admissible-velocity projection, and recovers the anchor reaction wrench. A planar case study illustrates the framework and motivates explicitly modeling external cables when estimating robot torques and control performance.
Problem
External welding umbilicals can influence robot motion and actuation forces, especially because lightweight and collaborative robots are more sensitive to external loads.
Method
The paper models the umbilical as a constrained serial multibody chain with passive elastic and dissipative joints, prescribed distal motion, and projected admissible-velocity dynamics.
Results
The formulation computes umbilical joint accelerations and explicitly recovers the reaction wrench exerted at the robot anchor point.
Takeaways & Limitations
The planar case study supports explicitly modeling external welding cables because neglecting them may produce significant errors in torque estimation and control performance.
Takeaways & Limitations
The model assumes passive joints whose torques arise solely from elastic stiffness and internal friction, and its dependent-coordinate solution assumes A_d is nonsingular.
Abstract
from arXiv · showhide
Robotic welding is widely used in industrial manufacturing, where the welding torch is often connected to the generator through an external umbilical. With the increasing deployment of lightweight and collaborative robots, the dynamic influence of this umbilical can significantly affect the robot motion and the actuation forces. This paper proposes a constrained multibody dynamic model of a welding umbilical, represented as a serial chain of rigid bodies interconnected by passive joints with elastic and dissipative effects. Prescribed motions at the distal anchor point are introduced through holonomic kinematic constraints. The equations of motion are reduced by projecting the dynamics onto the subspace of admissible velocities, yielding an efficient formulation free of Lagrange multipliers. The reaction wrench exerted by the umbilical on the robot is explicitly recovered. A planar case study illustrates the approach.
1 Introduction
External welding umbilicals are common but become dynamically significant for lightweight and collaborative robots. The paper situates its model among high-fidelity continuous approaches that can be computationally expensive.
- External welding umbilicals connect robot-mounted torches to welding generators and may be routed internally or externally along the robot structure.
- Lightweight and collaborative robots are more sensitive to external loads, making umbilical weight and stiffness relevant to robot dynamics.
- Continuous finite-element, geometrically exact beam, and Cosserat-rod models provide detailed cable representations but can produce computationally demanding formulations.
- The paper proceeds from general constrained multibody kinematics and dynamics to a planar case study and concluding perspectives.
2 Kinematics Model of the umbilical
The umbilical is represented as a serial chain of rigid bodies with generalized joint coordinates and frame assignments. Its distal motion is imposed through velocity-level kinematic constraints tied to the prescribed TCP motion.
- The umbilical consists of N+1 rigid bodies interconnected by N joints, with generalized coordinates q=(q_1,...,q_N)^T describing relative joint angles.
- Frames are attached to each body, while the base is fixed to the world frame and the distal body may be subject to prescribed motion.
- The constraint function uses the kinematic Jacobian A(q) to relate generalized velocities to the prescribed distal-anchor velocity twist V_E.
- The TCP frame follows the prescribed motions defined relative to the world, umbilical, and anchor-point frames.
3 Dynamic Model of the Umbilical
The dynamic formulation combines inertial, generalized-force, elastic, and friction effects in a constrained multibody model. Projection onto admissible velocities removes explicit multipliers for acceleration computation, after which the reaction wrench is recovered for robot coupling.
- The model uses an assembled Lagrangian equation with inertia M_0, generalized forces Q_0, joint torques τ, and constraint multipliers λ.
- Passive-joint torques arise from the umbilical’s elastic stiffness and internal friction, including Coulomb and viscous components.
- Newton–Euler recursion computes the inertia matrix and generalized internal forces while retaining computational efficiency and scalability with joint count.
- Dependent and independent joints are separated by decomposing A, with dependent velocities obtained from the constraint equations when A_d is nonsingular.
- Projection with H onto admissible velocities eliminates explicit Lagrange multipliers and yields a reduced linear system for independent joint accelerations.
- The full accelerations are reconstructed, and the Moore–Penrose-based multiplier solution recovers the generalized reaction wrench for coupling to robot dynamics.
4 Application to a Planar Case Study
The planar case study models the umbilical as a discretized inextensible bending chain and evaluates its coupled interaction with a 3-R robot. The setup includes catenary-based initialization, prescribed motion, and numerical integration of the coupled dynamics.
- Planar model: The umbilical is represented by N revolute joints and N+1 equal-length rigid links, equivalent to a planar Kirchhoff–Love beam for in-plane bending.Axial extension, compression, and transverse shear are neglected.
- Initialization and parameters: The simulation initializes the cable near its gravitational static equilibrium using a catenary approximation.The model uses N=10 joints, total length 1.54 m, linear mass density 2 kg m−1, bending stiffness 5 N m rad−1, and viscous friction 0.1 N m s rad−1.
- Initialization and parameters: The chosen discretization balances computational cost and deformation resolution, while increasing N did not significantly change the qualitative results.The parameter values were selected for industrial welding umbilicals, but were not experimentally identified.
- Numerical solution: The coupled system is integrated with a predictor–corrector scheme using a fixed time step of 0.5 ms.GMRES avoids explicit inversion of the potentially large and ill-conditioned matrix M𝛼1 for fine discretizations.
- Results: The study examines robot–umbilical configurations and compares the robot response within the planar interaction scenario.Figure 2 includes initial and intermediate configurations and a comparison involving the robot response.
- Results: Neglecting the external cable can produce significant errors in torque estimation and control performance, particularly for lightweight robots and dynamic trajectories.
5 Conclusions and future work
The paper presents a constrained multibody framework for modeling welding umbilicals and their interaction with robot manipulators. The planar case study shows that umbilical dynamics are non-negligible even when the cable is much lighter than the robot, motivating explicit inclusion in analysis and control.
- Contributions: The framework models the umbilical as rigid bodies connected by passive joints with elastic and dissipative effects, while enforcing distal-anchor motion through holonomic constraints.
- Contributions: Projecting the equations onto admissible velocities removes Lagrange multipliers and enables efficient computation of umbilical joint accelerations.
- Contributions: The formulation explicitly recovers the reaction wrench exerted by the umbilical on the robot.
- Conclusions: The planar case study demonstrates that umbilical dynamic effects remain non-negligible despite the umbilical having substantially less mass than the robot.
- Future work: The authors identify experimental validation as a focus of future work.