Elsevier

Automation in Construction

Volume 44, August 2014, Pages 12-24
Automation in Construction

Lift path planning for a nonholonomic crawler crane

https://doi.org/10.1016/j.autcon.2014.03.007Get rights and content

Highlights

  • The mobility and nonholonomic constraint is modeled into the path planning.

  • Strategies of sampling and expansion are used to efficiently obtain good path.

  • A metric in C-space is developed without any weight coefficients for each DOF.

  • The proposed approach can generate high-quality path in a short time.

  • Better paths may be obtained within shorter time by restricting the actions.

Abstract

This paper presents an efficient lift path planning approach for a crawler crane in which the mobility of the crawler crane and its nonholonomic kinematics are considered. To obtain the optimal path rapidly, we improved the bidirectional Rapidly exploring Random Trees (RRTs) using a sampling strategy and an expansion strategy. The sampling strategy of choosing a sample from a sampling pool and unexplored space was applied to guide trees towards the collision-free and high-quality region. Furthermore, the expansion strategy of extending one tree every other k steps was introduced to increase the chance of connecting to the other tree while ensuring that the trees have a small amount of nodes. The proposed approach was tested on three lift problems. The results indicate that the approach can generate high-quality paths in complex situations in a short time, and the paths satisfy the collision constraint, lifting capacity constraint and nonholonomic kinematics constraints of the crawler crane.

Introduction

Lift path planning is one of the most important subtasks during the heavy lift planning process. Informally, lift path planning generates a sequence of the cranes' motions, during which the cranes are not overloaded and do not collide with the lifted object and obstacles at the job sites. However, lift path planning is a challenging task because it requires considering the DOFs (degrees of freedom) of cranes, lifting capacity of cranes, kinematics of cranes and potential obstacles at job sites. Retrofit and expansion construction project sites tend to be especially congested, and finding a suitable lift path can be a difficult and tedious job. Without a path-planning tool, planning a lift path strongly depends on experienced lift engineers who choose cranes, position them and plan cranes' motions based on intuition and experience while not examining each possible alternative.

Fortunately, lift path planning has received extensive attention in recent years. Many methods are available for generating collision-free lift paths. Raghunatha and Varghese [10], [11] are early explorers who applied motion-planning thinking into lift path planning. In their work, a two-step search algorithm was proposed to plan the path of a single mobile crane. The first step consisted of determining the collision-free lift paths using a directed hill-climbing strategy, and the second search performs a more detailed optimization of the path within a constrained search space. Hill climbing and A* were then used to plan the path of cooperative crane lifts in Ref. [20]. The results of experiments show that A* was found near optimal paths but required considerably more time. In contrast, the hill climbing method was effective in generating feasible paths quickly, but the path was not optimal. Olearczyk et al. provided a method to plan the path of a single crane, which segmented the lifting process simplify control [13]. To reduce the computational time of planning, GA-based algorithms were used to plan the lift paths of two cranes working together [16], [17], [18], [19], [21]. In the research of Ref. [18], a GA algorithm was used and considered a better solution than the A* algorithm. However, one of the limits of the GA-based methods is that the paths are assumed to consist of a fixed number of configurations. To overcome this limitation, Xin Wang et al. utilized the Ant Colony algorithm to find a collision-free path for a mobile crane while considering both efficiency and safety [28]. In robotics, cranes are usually studied and treated as a robot. Thus, several advanced path-planning methods have been introduced in the area of lift path planning. For instance, Chang et al. developed a near real-time lift path planning method for single and dual crane erections [29]. They divided lift path planning into two phases: the first phase consisted of building the configuration space, which includes the crane's lift capacity and the obstacles at the job site; the second phase consists of finding a collision-free path in the generated C-space by using the probabilistic roadmap (PRM) method. As one of the most popular path planning algorithms in robotics, Rapidly exploring Random Trees (RRTs) [24] has been successfully used in numerous robotic systems [1], [7], [12], [14], [23], [30]. Recently, some researchers have introduced it into the lift path planning area. For example, Xin Wang et al. adopted a Bi-directional RRTs to plan a lift path for a single crawler crane in which hook rotating was taken into account [27]. For dynamic construction sites, Zhang et al. developed an RRT-based approach to monitor and re-plan the paths of cranes at construction sites using a real-time location system [4], [5], [6]. Subsequently, they proposed a motion-planning algorithm to efficiently generate safe and smooth paths for crane motions while considering the path smoothness and avoiding collisions [3]. Moreover, Lei et al. [32] presented another aspect to solve path planning; they considered the lifted object a robot and created the configuration space for different rotations of the lifting object on one specific elevation. Lei et al. proposed a generic method for mobile crane lifting binary (yes-or-no) path checking, in which the site constraints and the modules' erection orders are considered [31]. In addition, some researchers have focused on the lift path planning of tower cranes. Lee et al. presented a laser technology-based lifting-path tracking system for a robotic tower-crane [8] as well as a BIM- and sensor-based tower crane navigation system [9]. Kang and Miranda further proposed an incremental decoupled method to plan the motions of multiple tower cranes to avoid collision [22]. These studies have demonstrated the potential and value of utilizing a path-planning technique for crane lifts.

However, little information is available in the literature about lift path planning that considers the mobility (traveling and turning) of a crane. Previous studies have been limited to fixed base cranes and only considered the motions (slewing, luffing and hoisting) of the upper parts of a crane. In fact, this approach is inadequate in many real-world engineering projects. Thus, the traveling and turning must be adopted to complete the lift task when the placing position is far away from the picking position. Therefore, the mobility of a crane should be considered in lift path planning. Furthermore, the mobility of crawler crane was implemented by using a classic differential drive mechanism; thus, its kinematics are expressed as a differential constraint (nonholonomic constraint). Therefore, the path planning of such a complicated system is particularly challenging due to the high DOFs and nonholonomic kinematics constraint. To the author's knowledge, attempts have not been made to resolve this problem.

This paper aims to provide a lift path planning approach for a crawler crane that considers its mobility. Because the RRTs was specifically designed to handle nonholonomic constraints (including dynamics) and high DOFs, we used it to find a path in a given configuration space. To improve the quality of the path and the efficiency of path planning, we extended the RRTs algorithm first. The nonholonomic kinematics constraint of a crawler crane is modeled in the proposed approach. The results of experiments illustrated that our approach can find a feasible lift path that satisfies the collision constraint, lifting capacity constraint and nonholonomic constraint of the mobility of the crawler crane. The approach can help planners to rapidly generate initial feasible lift paths in the stage of developing a detailed lift plan and can be used to generate an alternative lift path within a short period when last-minute changes are made to the constraints. One limitation of this research is that the proposed method does not consider the swing of lifting ropes, which may lead to a safety issue. Furthermore, this study primarily focuses on the lift path planning that requires the motions of the base of a crane. Furthermore, we only examined the example of a crawler crane with a main boom for the sake of convenience.

Section snippets

Problem formulation

Informally, the problem of path planning of a crawler crane is defined as follows: given the picking configuration and placing configuration of crawler crane, find a safe motion sequence at the construction site that contains obstacles so that the crawler crane is under its capacity and is collision-free along with the motion sequence. The path found must meet three requirements: 1) the crawler cranes, the lifted object and obstacles do not collide; 2) the crawler crane must be not overloaded;

Overview of the approach

In this study, we planned the lift path by using the bidirectional RRTs, which searches a path in the configuration space (C-space). Its flowchart is shown as Fig. 1. First, the information, including the model of the lifting environment, the model and weight of the lifting load, the model and loading capacity of the crane, the picking configuration and the placing configuration of the crane, must be provided to the planner. Second, the C-space of the crawler crane is constructed according to

Implementation

Because the idea of the proposed approach was addressed in Section 3, we will introduce its implementation in this section. The main frame of the approach is shown in Algorithm 1, which contains two operations (ChooseSample and Connect).

Algorithm 1

Algorithm 2

Algorithm 3

Algorithm 1 elaborates the overview of the proposed approach, described in Section 3.1. Algorithm 2 illustrates the implementation of the sampling strategy. The proposed algorithm provides sampling pools for the two trees, denoted as SPinit and SPgoal,

Experiments and discussion

Three validation studies have been conducted to assess (1) the usability and effectiveness of the proposed approach for a crawler crane lift and (2) the efficiency of the developed approach. The tests were performed on a Thinkpad T60 2.0 GHz computer with 1 GB of memory. A prototypical visualization system was developed to visually display the lift path. The visualization system can visualize the motions of the mobile crane along the lift path. It was built using the Visual C++ 2005 compiler with

Contributions of this research

A planning approach to generate a lift path for a crawler crane was developed. The main contributions of this research are the following:

  • 1)

    The mobility of crawler cranes and its nonholonomic constraint are considered in the approach. The lift path is more natural and can be used to control the crane.

  • 2)

    A metric of two configurations in the C-space and a path length function were developed without weight coefficients for each degree of freedom. Moreover, the definition of the metric has obvious

Conclusions and future work

In this study, we proposed an efficient lift path planning approach for a crawler crane, in which the mobility of the crane and its nonholonomic kinematics constraint were considered. First, we formulated the problem of lift path planning for a crawler crane. The overview of the proposed approach was the elaborated, and several strategies were introduced into the approach. The proposed approach can quickly find an initial feasible suboptimal path by using the sampling strategy and the tree

Acknowledgments

This work is supported by the Liaoning Province Natural Science Fund (201102025), the Fundamental Research Funds for the Central Universities (DUT14ZD221), and the Dalian Science and Technology Plan Project (2012A17GX122 and 2013A16GX111).

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