Coordinated Manipulation of Hybrid Deformable-Rigid Objects in Constrained Environments

Abstract

Coordinated robotic manipulation of deformable linear objects (DLOs), such as ropes and cables, has been widely studied; however, handling hybrid assemblies composed of both deformable and rigid elements in constrained environments remains challenging. This work presents a quasi-static optimization-based manipulation planner that employs a strain-based Cosserat rod model, extending rigid-body formulations to hybrid deformable linear objects (hDLO). The proposed planner exploits the compliance of deformable links to maneuver through constraints while achieving task-space objectives for the object that are unreachable with rigid tools. By leveraging a differentiable model with analytically derived gradients, the method achieves up to a 33x speedup over finite-difference baselines for inverse kinetostatic(IKS) problems. Furthermore, the subsequent trajectory optimization problem, warm-started using the IKS solution, is only practically realizable via analytical derivatives. The proposed algorithm is validated in simulation on various hDLO systems and experimentally on a three-link hDLO manipulated in a constrained environment using a dual-arm robotic system. Experimental results confirm the planner's accuracy, yielding an average deformation error of approximately 3 cm (5% of the deformable link length) between the desired and measured marker positions. Finally, the proposed optimal planner is compared against a sampling-based feasibility planner adapted to the strain-based formulation. The results demonstrate the effectiveness and applicability of the proposed approach for robotic manipulation of hybrid assemblies in constrained environments.

Figures (10)

• Figure 1: Overview of the robotic platform and an example assembly of deformable and rigid links. The goal of this paper is to generate a quasi-static trajectory that reaches a desired goal while satisfying the workspace (environmental) constraints represented by the red circles.
• Figure 2: Schematics of exemplary hDLO systems. The depicted hDLO, composed of two DLOs, is actuated via aerial vehicles, prismatic and revolute joints, or serial manipulators with multiple revolute joints.
• Figure 3: The pose of the cross section is computed at finite computational points denoted by $X_j$. At other points, we approximate the pose via an interpolation in $SE(3)$ by assuming a constant twist between two consecutive computational points. Interpolation is described in Algorithm \ref{['Algorithm_interp']}.
• Figure 4: Deformable-rigid assembly examples: a) Deformable and rigid links, connected by a fixed link. b) Deformable rigid links, connected by spherical joints represented by a yellow circle. c) Two deformable and single rigid links d) Three deformable and two rigid links, connected by spherical joints.
• Figure 5: Moving from the same initial configuration of the robot, we need to make use of the deformation of the hDLO to move to the desired pose within the hole constraints. a) shows the trajectory when constraints are considered. b) shows the trajectory when the constraints are not considered.