Coordinated Manipulation of Hybrid Deformable-Rigid Objects in Constrained Environments
Authors: Anees Peringal, Anup Teejo Mathew, Panagiotis liatsis, Federico Renda
Organizations: Department of Mechanical and Nuclear Engineering, Khalifa University, Abu Dhabi, UAE, and also with the Khalifa University Center for Autonomous Robotic Systems (KUCARS), Khalifa University, Abu Dhabi, UAE · Department of Computer Science, Khalifa University, Abu Dhabi, UAE
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 & tables
Fig. 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.
Fig. 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.
Fig. 3 : The pose of the cross section is computed at finite computational points denoted by Xj . 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 1 .
Fig. 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.
Component
Parameter
Value
DLO (Nitinol)
Length
0.68m
Outer diameter
1.8mm
Inner diameter
1.4mm
Young’s modulus
7.5\times1010Pa
Poisson ratio
0.33
Density
6450kgm−3
TABLE I : Geometric and material properties of the assembly components used in the simulation.
Fig. 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.
Fig. 6 : TO planner is extended to other hDLOs in Fig 4 (b), (c) and (d) respectively. The desired position for hDLO (b) is shown by the blue point and similarly the desired poses for other hDLOs are shown with the axes.
Assembly
nd
na
nc
Time taken (s)
Iteration count
a
62
14
6
27.66
221
b
68
14
6
52.88
141
c
90
18
12
53.38
132
d
93
18
12
55.18
102
TABLE II : The time taken to generate the trajectories shown in Fig. 5 (a) and Fig. 6 .
Fig. 7 : Experimental validation of the hDLO-manipulator model. The average error between the markers in experiment and simulation is 3.07% of the deformable object length.
Fig. 8 : The unconstrained path planning is compared with the experiment. We find that the average error between the planned marker positions and those measured from the experiment is 2.6 cm or 3.7% of the deformable object length.
Fig. 9 : Constrained trajectory planning is compared with the experiment. The markers measured in the experiment are shown in green, and the markers in the simulation are shown in red. We find an average error of 0.0202m.
Constrained error
Unconstrained error
Trajectory
Average (cm)
Final (cm)
Avg (cm)
Final(cm)
1
1.37(2.01%)
2.62
1.95(2.87%)
1.41
2
1.68(2.47%)
2.14
1.64(2.41%)
2.16
3
2.18(3.20%)
7.53
3.71(5.45%)
4.87
4
2.60(3.82%)
3.66
2.82(4.14%)
2.78
TABLE III : Average error between the planned path and the measured path, expressed both in centimeters and as a percentage of the length of one Nitinol rod.
Trajectory number
BiRRT
TO
1
33.56 (4.52)
42.36
2
12.34 (4.50)
40.00
3
201.69 (14.39)
45.65
4
39.77 (2.96)
33.64
TABLE IV : Time to convergence between our TO method and BiRRT method inspired by the literature. To account for the stochastic nature of BiRRT, each trajectory is run 5 times to get the mean and standard deviation (in brackets) of the computation time.
Fig. 10 : The trajectories computed from the TO (left) and the BiRRT (right) are compared. The TO approach finds a smoother trajectory in generalized coordinates and actuation forces.
Technical University of Darmstadt · School of Electrical and Computer Engineering, Universidade Estadual de Campinas (UNICAMP), Brazil · Instituto de Pesquisas Eldorado, Brazil +5