Elsevier

Journal of Manufacturing Systems

Volume 57, October 2020, Pages 158-168
Journal of Manufacturing Systems

An algorithm based on bidirectional searching and geometric constrained sampling for automatic manipulation planning in aircraft cable assembly

https://doi.org/10.1016/j.jmsy.2020.08.015Get rights and content

Highlights

  • An improved RRT algorithm for robotic cable assembly planning is proposed.

  • Geometric constraints for generating sampling nodes improve sampling efficiency.

  • Bidirectional searching avoids narrow passage problems in planning.

  • Planning time costs decrease by 90 % with proposed algorithm.

Abstract

Robotic manipulation of deformable linear objects has potential application in aircraft cable assembly. However, it is difficult to be implemented in real tasks due to requiring prediction of the object’s deformation and obstacle-free manipulation planning with high efficiency. Aiming at exploring automatic assembly planning for aircraft cables assembly in narrow cabins with obstacles, this paper proposes a novel planning algorithm named RRT-BwC (Bi-direction with Constrain). Firstly, formulation of the question and the manipulation objects are presented with geometric definitions. Then a bi-RRT-tree searching method is developed to design the planner for overcoming obstacles in the high dimensional planning space. The numerical distance between configurations in the cable shape space are defined to measure the demands for their transition in consideration of the manipulation logics. And the sampling zone constrains to the shape configuration nodes are also discussed. Finally, the algorithm presents a valid manipulation sequence for robotic manipulation. The functionality and performance of the improved RRT approach are demonstrated with a simulated real-world problem of aircraft cable assembly, exhibiting computation efficiency promotion.

Introduction

Deformable linear objects (DLOs) such as cables, hoses and wire harnesses are widely distributed in modern large-scale aircrafts. Cables usually contain a set of wires with ties, clamps, plugs and auxiliary parts. The cable configurations before and after assembly are shown in Fig.1. Before assembly, cables present completely loose, and they will be attached to rigid support structures through a series of anchor points and clamps during the final system assembly process. In order to accomplish the configuration transition, a series of basic tasks such as distinguishing cables, localizing anchor parts/clamps, moving/installing cables should be performed. The main actions should be taken for the assembly tasks involve bending/moving cables through grasping specific points, installing the anchor points on cables to the corresponding fixed clamp parts and inserting terminal plugs to the corresponding products according to the engineering drawings and guidance documents. Thus the flexible parts will be shaped into specific curves. Meanwhile, obstacle bypassing and over-stretch avoidance should be taken into consideration. Such manipulation tasks can be classified into geometrical manipulation in contrast to topological manipulation [1].

In the past few decades, digital assembly and measurement technologies have found an increasingly wide application in aircraft manufacturing. But these explorations mainly focus on alignment of position and orientation for rigid components. The cable routing and installation is usually carried out manually [2]. However, cable assembly tasks in this process are hard and tedious for human workers due to the numerous similar linear objects and narrow cabins with poor accessibility and ergonomic conditions (Fig. 2). As a consequence, final assembly of aircraft systems are time-consuming and burdensome, for instance, A380 production was delayed because of electrical cable harnesses assembly [3].

As robotic manipulation has gained its popularity in automatic production, robotic manipulating of DLOs is regarded as a promising solution for aircraft cable assembly [1]. There are two vital topics among current researches on DLOs, especially on preparation works for DLOs manipulation: efficient and accurate shape modeling; robust and universal manipulation planning.

As for shape modeling problem, there are multiple methods to model DLOs. For example, spring-mass model has been employed for cable assembly simulation as a typical discrete modeling method [4]. Due to its physical interpretability and directness, minimal energy method is preferred in modeling and simulation of DLOs. As early as 1990s, Hirai et al. [5] formulated the curve shape expression as a linear combination of a set of basic functions with differential geometry, and solved it by optimizing the linear parameters to minimize the total potential energy along the curve. These researchers aimed to model cables with fixed length and verified its stability. Moll et al. [6] presented a subdivision scheme for computing minimal-energy curves with manipulation constrains, and introduced a planner to generate stable intermediate configurations transiting from one shape configuration to another. Splines have also been applied in the DLO simulation questions for its simplicity. Ma [7] simulated a wire harness with a cubic spline curve. The length constrains are satisfied through iteration and efficiency of the real-time interactive algorithm reached 24 Hz. Bretl and McCarthy [8] modeled the DLO to a Kirchhoff rod, and proposed that the set of solutions for such a DLO configuration was a smooth manifold of finite dimension which could be parameterized by a single coordinate chart. Lv and Ding [9] modeled DLO based on the Cosserat theory of elastic rods, in which the multi-branch cables and their joints simulation were settled. Shah et al. [10,11] treated the multiple interlinked DLO modeling problem as an optimal control question, and solved it with a boundary value problem(BVP) solver. The invariance for length and stiffness transformation has also been verified.

Considering the computation difficulty of deformable object simulation and unknown factors involved in deformation, physical-model-free methods have been explored with the development of vision technologies. Berenson [12] estimated the visual Jacobian of manipulating DLOs by exploiting diminishing rigidity hypothesis without explicit models to the objects. The local manipulation problem was settled in [12]. Abbeel et al. [13] proposed a self-supervised CNN (Convolutional Neural Network) learning scheme to link the image state of the rope with the robotic manipulating action. The goal-directed inverse dynamic model was validated by robotic manipulation experiments.

Currently, manipulation planning for DLOs can be roughly divided into two categories: learning from demonstration/data (LfD) and automatic planning. Rambow [14] presented an approach to generalize human demonstrations on flexible pipe manipulation to robots. The control scheme was made up with a demonstration reference trajectory and appropriate feedback control. Han [15] applied an unsupervised model-based learning method PILCO (Probabilistic Inference for Learning Control) to settle the high dimension problems of DLO manipulation and demonstrated its effect. Wang and Abbeel [16] separated the DLO manipulation task into visual planning and acting. In the former block, a GAN (Generative Adversarial Network)-based paradigm was proposed to generate manipulation trajectories for the DLO in image space, which possessed interpretability and visualization. Learning-based methods have fewer requirements for physical parameters and models, but their performances shrink when being generalized to trivial scenes deviating from the given data. As for automatic planning, Jiang and Uchiyama [17,18] made several engineering explorations to practical wire harness assembly system for vehicle production, including anchor points realization, action designing and fixation to the wires. Experiments have been made with a multi-arm robot system and an instrumental panel frame. Qin [19] introduced humanoid robots to install a cable between two aircraft clamps with integration of STRIPS (Stanford Research Institute Problem Solver), walking controller and motion controller. A prototype algorithm was also developed to generate a manipulation sequence for installing large-scale interlinked cables into an aircraft fuselage with the concern for interlink over-stretch constrains, and time complexity of the planner was analyzed [10,11].

In the field of planning research, sampling-based approaches make a great contribution due to their adaptability; PRM (Probabilistic Roadmap Planner) and RRT (Rapid-exploring Random Tree) are typical algorithms among them. PRM had an early application in path planning for deformable linear objects [20] in 1996, and the following papers [6,8] extended its employment. In recent years, numerous RRT-based variant schemes have been proposed to promote the efficiency and applicability. In [21] retraction RRT algorithm and decomposition planner are combined to accomplish motion planning for high DOF (degree-of-freedom) articulated objects. In [[22], [23], [24], [25]], flexible wire or cable objects manipulation problems were formulated, and improved RRT-based methods were employed to generate assembly paths for flexible parts under environment constrains.

However, there are still problems unsolved with state-of-the-arts. In large aircrafts, there exist quantities of cables which are designed to be assembled in narrow cabins with poor accessibility, and such installation tasks remain challenging. Though literatures have reported explorations to plan paths for cables of which both ends are held, aircraft cables have more anchor points in the middle besides two endpoints, which also needs to be controlled, so the dimensions of the planning space increase. In addition, previous research usually plans the assembly path for cables with a series of levitating configurations, and the feasibility of such shape configurations with limited manipulators is ignored [24,25]. Meanwhile, most of such manipulation planning methods aimed at manipulation tasks in the open space with multi-arm robot system involved in, but tasks with multiple anchor points in small spaces with manifold obstacles are little considered, which is exactly a challenge in aircraft cable assembly.

The prerequisite of robotic assembly is planning a manipulation path to determine each action type for the robot to perform, through which the cable configuration transitions in Fig.1 accomplish.

This paper is exactly motivated by the manipulation path planning problem in aircraft cable assembly in unreachable cabins. An RRT-based algorithm named (RRT-BwC) is proposed to plan manipulation path to accomplish the cable assembly tasks, which provides not only an obstacle-free assembly path for the cable, but also a manipulation sequence that can be used to guide the robot movements. Compared with time-consuming baselines faced with the scenario, in the algorithm, the constrained sampling tactics and bi-random-exploring-tree scheme are raised to promise the planning method with high efficiency.

The remainder of the paper is organized as following. Section 2 presents a formulated definition of the cable assembly task. In Section 3, we describe the technique used to model the deformable linear objects. In Section 4, the sampling-based planning algorithm is explained in detail. The effect of the algorithm and comparison with baselines are demonstrated with simulations to an assembly problem in Section 5. The paper ends up with discussion and future work in Section 6.

Section snippets

Question statement

Manipulation planning for cable assembly can be framed as a path planning question in the DLO shape configuration space. The planning space can be defined as

, where each node represents a DLO shape configuration. The configurations can transit from one state to another through human or robot manipulations. In the workspace, flexible or rigid parts apart from the manipulated cable are ubiquitous, which can be considered as obstacles, including walls, beams, frames and narrow doorway of the

Model

In this paper, the spline method [7] and the classical minimal-energy theory is used to model and simulate DLOs with high computation efficiency. The model is built under quasi-static condition. The total potential energy to be minimized is:U=0L12kX'(s)2+12bX''(s)2+ρgz(s)ds+0L12rT(s)2ds

In (7) k, b and r are the parameters characterizing flexibility of the cable. They can be deduced with elasticity modulus, shear modulus, density and diameter of the cable as: k = EA =ρEd2/4, b = ρEd4/64, r =

Algorithm

RRT is a typical sampling-based planning method. Among numerous collision-avoidance planning methods, sampling-based algorithms such as RRT and PRM have been employed on cable routing/virtual assembly planning problems due to their adaptability with high-dimension; and their feasibility on such questions has already been proved through cases in literatures. Compared with PRM, there is no need in RRT for pre-processing obstacles and complex environments to build the roadmap, which is quite

Evaluations

The model of the real-world aircraft cable assembly is shown in Fig.6 and the initial state of the cable is shown in Fig. 13. The clamps and installed cable besiege the obstacle beam. The total length of the cable model is above 665 mm, with 6 anchor points located on it. The clamps are aligned in a three-dimensional array rather than a planar structure. The length between the neighboring two anchor points is 1.1 times with respect to the distance between the corresponding clamps, i.e. there is

Conclusion

This paper proposed a sampling-based algorithm RRT-BwC to generate robotic manipulation scheme for aircraft cable assembly in narrow cabins. The mathematical descriptions for the task space, manipulated objects, transition actions and relevant constrains are presented in detail. A distance value measuring the similarity of the two cable configurations is defined to steer rapid-exploring random trees to grow and prevent redundant manipulations. The bi-directional searching structure and

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The work is supported by the National Natural Science Foundation of China, Grant No. 51575306.

References (27)

  • T. Bretl et al.

    Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations

    Int J Rob Res

    (2014)
  • A.J. Shah et al.

    Towards manipulation planning for multiple interlinked deformable linear objects

    IEEE International Conference on Robotics and Automation

    (2016)
  • A. Shah et al.

    Planning for manipulation of interlinked deformable linear objects with applications to aircraft assembly

    IEEE Trans Autom Sci Eng

    (2018)
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