Multi-objective Anti-swing Trajectory Planning of Double-pendulum Tower Crane Operations using Opposition-based Evolutionary Algorithm

Underactuated tower crane lifting requires time-energy optimal trajectories for the trolley/slew operations and reduction of the unactuated swings resulting from the trolley/jib motion. In scenarios involving non-negligible hook mass or long rig-cable, the hook-payload unit exhibits double-pendulum behaviour, making the problem highly challenging. This article introduces an offline multi-objective anti-swing trajectory planning module for a Computer-Aided Lift Planning (CALP) system of autonomous double-pendulum tower cranes, addressing all the transient state constraints. A set of auxiliary outputs are selected by methodically analyzing the payload swing dynamics and are used to prove the differential flatness property of the crane operations. The flat outputs are parameterized via suitable B\'{e}zier curves to formulate the multi-objective trajectory optimization problems in the flat output space. A novel multi-objective evolutionary algorithm called Collective Oppositional Generalized Differential Evolution 3 (CO-GDE3) is employed as the optimizer. To obtain faster convergence and better consistency in getting a wide range of good solutions, a new population initialization strategy is integrated into the conventional GDE3. The computationally efficient initialization method incorporates various concepts of computational opposition. Statistical comparisons based on trolley and slew operations verify the superiority of convergence and reliability of CO-GDE3 over the standard GDE3. Trolley and slew operations of a collision-free lifting path computed via the path planner of the CALP system are selected for a simulation study. The simulated trajectories demonstrate that the proposed planner can produce time-energy optimal solutions, keeping all the state variables within their respective limits and restricting the hook and payload swings.Comment: 14 pages, 14 figures, 6 table

Control of free-ranging automated guided vehicles in container terminals

Container terminal automation has come to the fore during the last 20 years to improve their efficiency. Whereas a high level of automation has already been achieved in vertical handling operations (stacking cranes), horizontal container transport still has disincentives to the adoption of automated guided vehicles (AGVs) due to a high degree of operational complexity of vehicles. This feature has led to the employment of simple AGV control techniques while hindering the vehicles to utilise their maximum operational capability. In AGV dispatching, vehicles cannot amend ongoing delivery assignments although they have yet to receive the corresponding containers. Therefore, better AGV allocation plans would be discarded that can only be achieved by task reassignment. Also, because of the adoption of predetermined guide paths, AGVs are forced to deploy a highly limited range of their movement abilities while increasing required travel distances for handling container delivery jobs. To handle the two main issues, an AGV dispatching model and a fleet trajectory planning algorithm are proposed. The dispatcher achieves job assignment flexibility by allowing AGVs towards to container origins to abandon their current duty and receive new tasks. The trajectory planner advances Dubins curves to suggest diverse optional paths per origin-destination pair. It also amends vehicular acceleration rates for resolving conflicts between AGVs. In both of the models, the framework of simulated annealing was applied to resolve inherent time complexity. To test and evaluate the sophisticated AGV control models for vehicle dispatching and fleet trajectory planning, a bespoke simulation model is also proposed. A series of simulation tests were performed based on a real container terminal with several performance indicators, and it is identified that the presented dispatcher outperforms conventional vehicle dispatching heuristics in AGV arrival delay time and setup travel time, and the fleet trajectory planner can suggest shorter paths than the corresponding Manhattan distances, especially with fewer AGVs.Open Acces

Safe distance prediction for braking control of bridge cranes considering anti-swing

Cranes are widely deployed for lifting and moving heavy objects in dynamic environments with human coexistence. Suddenly appeared workers, vehicles, and robots can affect the safety of the cranes. To avoid possible collisions, the cranes must have prediction ability to know how dangerous the situation is. In this paper, we address the safety issues of bridge cranes based on its online physical states and control model. Due to the swing of the payload, the safe braking distance cannot be a constant value. Therefore, we here propose a model prediction control (MPC)-based anti-swing method for non-zero initial states, where a new reference trajectory and a new cost function for optimization are proposed, such that the proposed MPC method can control the crane to follow the proposed reference trajectory and achieve a stable stop state with anti-swing. Furthermore, an offline learning mechanism is introduced to learn a statistical model between the velocity of the crane and the safe braking distance achieved by using the proposed MPC braking control method. In this way, we can predict how far the crane would require to safely stop without swing based on its current velocity, which is the safe distance prediction to evaluate the dangerous level of the dynamic obstacle. Experiments using both a simulated crane and a real crane demonstrate that the proposed safe braking distance prediction method is effective for safe braking control of the bridge cranes

Proceedings of the 4th Baltic Mechatronics Symposium - Tallinn April 25, 2019

The Baltic Mechatronics Symposium is annual symposium with the objective to provide a forum for young scientists from Baltic countries to exchange knowledge, experience, results and information in large variety of fields in mechatronics. The symposium was organized in co-operation with Taltech and Aalto University. The venue of the symposium was Nordic Hotel Forum Tallinn.The symposium was organized parallel to the 12th International DAAAM Baltic Conference and 27th International Baltic Conference BALTMATTRIB 2019. The selected papers are published in Proceedings of Estonian Academy of Sciences indexed in ISI Web of Science. The content of the proceedings: 1. Continuous wet spinning of cellulose nanofibrils 2. Development of motor efficiency test setup for direct driven hydraulic actuator 3. Development of pressure former for continuous nanopaper manufacturing 4. Device for tree volume measurements 5. Effect of external load on rotor vibration 6. Granular jamming based gripper for heavy objects 7. Integrated car camera system for monitoring inner cabin and outer traffic 8. Inverted pendulum controlled with CNC control system 9. Multi-material mixer and extruder for 3D printing 10. Object detection and trajectory planning using a LIDAR for an automated overhead cran

Efficient Mission Planning for Robot Networks in Communication Constrained Environments

Many robotic systems are remotely operated nowadays that require uninterrupted connection and safe mission planning. Such systems are commonly found in military drones, search and rescue operations, mining robotics, agriculture, and environmental monitoring. Different robotic systems may employ disparate communication modalities such as radio network, visible light communication, satellite, infrared, Wi-Fi. However, in an autonomous mission where the robots are expected to be interconnected, communication constrained environment frequently arises due to the out of range problem or unavailability of the signal. Furthermore, several automated projects (building construction, assembly line) do not guarantee uninterrupted communication, and a safe project plan is required that optimizes collision risks, cost, and duration. In this thesis, we propose four pronged approaches to alleviate some of these issues: 1) Communication aware world mapping; 2) Communication preserving using the Line-of-Sight (LoS); 3) Communication aware safe planning; and 4) Multi-Objective motion planning for navigation. First, we focus on developing a communication aware world map that integrates traditional world models with the planning of multi-robot placement. Our proposed communication map selects the optimal placement of a chain of intermediate relay vehicles in order to maximize communication quality to a remote unit. We also vi propose an algorithm to build a min-Arborescence tree when there are multiple remote units to be served. Second, in communication denied environments, we use Line-of-Sight (LoS) to establish communication between mobile robots, control their movements and relay information to other autonomous units. We formulate and study the complexity of a multi-robot relay network positioning problem and propose approximation algorithms that restore visibility based connectivity through the relocation of one or more robots. Third, we develop a framework to quantify the safety score of a fully automated robotic mission where the coexistence of human and robot may pose a collision risk. A number of alternate mission plans are analyzed using motion planning algorithms to select the safest one. Finally, an efficient multi-objective optimization based path planning for the robots is developed to deal with several Pareto optimal cost attributes

Advanced Discrete-Time Control Methods for Industrial Applications

This thesis focuses on developing advanced control methods for two industrial systems in discrete-time aiming to enhance their performance in delivering the control objectives as well as considering the practical aspects. The first part addresses wind power dispatch into the electricity network using a battery energy storage system (BESS). To manage the amount of energy sold to the electricity market, a novel control scheme is developed based on discrete-time model predictive control (MPC) to ensure the optimal operation of the BESS in the presence of practical constraints. The control scheme follows a decision policy to sell more energy at peak demand times and store it at off-peaks in compliance with the Australian National Electricity Market rules. The performance of the control system is assessed under different scenarios using actual wind farm and electricity price data in simulation environment. The second part considers the control of overhead crane systems for automatic operation. To achieve high-speed load transportation with high-precision and minimum load swings, a new modeling approach is developed based on independent joint control strategy which considers actuators as the main plant. The nonlinearities of overhead crane dynamics are treated as disturbances acting on each actuator. The resulting model enables us to estimate the unknown parameters of the system including coulomb friction constants. A novel load swing control is also designed based on passivity-based control to suppress load swings. Two discrete-time controllers are then developed based on MPC and state feedback control to track reference trajectories along with a feedforward control to compensate for disturbances using computed torque control and a novel disturbance observer. The practical results on an experimental overhead crane setup demonstrate the high performance of the designed control systems.Comment: PhD Thesis, 230 page

해양 작업 지원선의 자율 운항 및 설치 작업 지원을 위한 시뮬레이션 방법

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 조선해양공학과, 2019. 2. 노명일.Autonomous ships have gained a huge amount of interest in recent years, like their counterparts on land{autonomous cars, because of their potential to significantly lower the cost of operation, attract seagoing professionals and increase transportation safety. Technologies developed for the autonomous ships have potential to notably reduce maritime accidents where 75% cases can be attributed to human error and a significant proportion of these are caused by fatigue and attention deficit. However, developing a high-level autonomous system which can operate in an unstructured and unpredictable environment is still a challenging task. When the autonomous ships are operating in the congested waterway with other manned or unmanned vessels, the collision avoidance algorithm is the crucial point in keeping the safety of both the own ship and any encountered ships. Instead of developing new traffic rules for the autonomous ships to avoid collisions with each other, autonomous ships are expected to follow the existing guidelines based on the International Regulations for Preventing Collisions at Sea (COLREGs). Furthermore, when using the crane on the autonomous ship to transfer and install subsea equipment to the seabed, the heave and swaying phenomenon of the subsea equipment at the end of flexible wire ropes makes its positioning at an exact position is very difficult. As a result, an Anti-Motion Control (AMC) system for the crane is necessary to ensure the successful installation operation. The autonomous ship is highly relying on the effectiveness of autonomous systems such as autonomous path following system, collision avoidance system, crane control system and so on. During the previous two decades, considerable attention has been paid to develop robust autonomous systems. However, several are facing challenges and it is worthwhile devoting much effort to this. First of all, the development and testing of the proposed control algorithms should be adapted across a variety of environmental conditions including wave, wind, and current. This is one of the challenges of this work aimed at creating an autonomous path following and collision avoidance system in the ship. Secondly, the collision avoidance system has to comply with the regulations and rules in developing an autonomous ship. Thirdly, AMC system with anti-sway abilities for a knuckle boom crane remains problems regarding its under-actuated mechanism. At last, the performance of the control system should be evaluated in advance of the operation to perform its function successfully. In particular, such performance analysis is often very costly and time-consuming, and realistic conditions are typically impossible to establish in a testing environment. Consequently, to address these issues, we proposed a simulation framework with the following scenarios, which including the autonomous navigation scenario and crane operation scenario. The research object of this study is an autonomous offshore support vessel (OSV), which provides support services to offshore oil and gas field development such as offshore drilling, pipe laying, and oil producing assets (production platforms and FPSOs) utilized in EP (Exploration Production) activities. Assume that the autonomous OSV confronts an urgent mission under the harsh environmental conditions: on the way to an imperative offshore construction site, the autonomous OSV has to avoid target ships while following a predefined path. When arriving at the construction site, it starts to install a piece of subsea equipment on the seabed. So what technologies are needed, what should be invested for ensuring the autonomous OSV could robustly kilometers from shore, and how can an autonomous OSV be made at least as safe as the conventional ship. In this dissertation, we focus on the above critical activities for answering the above questions. In the general context of the autonomous navigation and crane control problem, the objective of this dissertation is thus fivefold: • Developing a COLREGs-compliant collision avoidance system. • Building a robust path following and collision avoidance system which can handle the unknown and complicated environment. • Investigating an efficient multi-ship collision avoidance method enable it easy to extend. • Proposing a hardware-in-the-loop simulation environment for the AHC system. • Solving the anti-sway problem of the knuckle boom crane on an autonomous OSV. First of all, we propose a novel deep reinforcement learning (RL) algorithm to achieve effective and efficient capabilities of the path following and collision avoidance system. To perform and verify the proposed algorithm, we conducted simulations for an autonomous ship under unknown environmental disturbance iiito adjust its heading in real-time. A three-degree-of-freedom dynamic model of the autonomous ship was developed, and the Line-of-sight (LOS) guidance system was used to converge the autonomous ship to follow the predefined path. Then, a proximal policy optimization (PPO) algorithm was implemented on the problem. By applying the advanced deep RL method, in which the autonomous OSV learns the best behavior through repeated trials to determine a safe and economical avoidance behavior in various circumstances. The simulation results showed that the proposed algorithm has the capabilities to guarantee collision avoidance of moving encountered ships while ensuring following a predefined path. Also, the algorithm demonstrated that it could manage complex scenarios with various encountered ships in compliance with COLREGs and have the excellent adaptability to the unknown, sophisticated environment. Next, the AMC system includes Anti-Heave Control (AHC) and Anti-Sway Control (ASC), which is applied to install subsea equipment in regular and irregular for performance analysis. We used the proportional-integral-derivative (PID) control method and the sliding mode control method respectively to achieve the control objective. The simulation results show that heave and sway motion could be significantly reduced by the proposed control methods during the construction. Moreover, to evaluate the proposed control system, we have constructed the HILS environment for the AHC system, then conducted a performance analysis of it. The simulation results show the AHC system could be evaluated effectively within the HILS environment. We can conclude that the proposed or adopted methods solve the problems issued in autonomous system design.해양 작업 지원선 (Offshore Support Vessel: OSV)의 경우 극한의 환경에도 불구하고 출항하여 해상에서 작업을 수행해야 하는 경우가 있다. 이러한 위험에의 노출을 최소화하기 위해 자율 운항에 대한 요구가 증가하고 있다. 여기서의 자율 운항은 선박이 출발지에서 목적지까지 사람의 도움 없이 이동함을 의미한다. 자율 운항 방법은 경로 추종 방법과 충돌 회피 방법을 포함한다. 우선, 운항 및 작업 중 환경 하중 (바람, 파도, 조류 등)에 대한 고려를 해야 하고, 국제 해상 충돌 예방 규칙 (Convention of the International Regulations for Preventing Collisions at Sea, COLREGs)에 의한 선박간의 항법 규정을 고려하여 충돌 회피 규칙을 준수해야 한다. 특히 연근해의 복잡한 해역에서는 많은 선박을 자동으로 회피할 필요가 있다. 기존의 해석적인 방법을 사용하기 위해서는 선박들에 대한 정확한 시스템 모델링이 되어야 하며, 그 과정에서 경험 (experience)에 의존하는 파라미터 튜닝이 필수적이다. 또한, 회피해야 할 선박 수가 많아질 경우 시스템 모델이 커지게 되고 계산 양과 계산 시간이 늘어나 실시간 적용이 어렵다는 단점이 있다. 또한, 경로 추종 및 충돌 회피를 포함하여 자율 운항 방법을 적용하기가 어렵다. 따라서 본 연구에서는 강화 학습 (Reinforcement Learning: RL) 기법을 이용하여 기존 해석적인 방법의 문제점을 극복할 수 있는 방법을 제안하였다. 경로를 추종하는 선박 (agent)은 외부 환경 (environment)과 상호작용하면서 학습을 진행한다. State S_0 (선박의 움직임과 관련된 각종 상태) 가지는 agent는 policy (현재 위치에서 어떤 움직임을 선택할 것인가)에 따라 action A_0 (움직일 방향) 취한다. 이에 environment는 agent의 다음 state S_1 을 계산하고, 그에 따른 보상 R_0 (해당 움직임의 적합성)을 결정하여 agent에게 전달한다. 이러한 작업을 반복하면서 보상이 최대가 되도록 policy를 학습하게 된다. 한편, 해상에서 크레인을 이용한 장비의 이동이나 설치 작업 시 위험을 줄이기 위해 크레인의 거동 제어에 대한 요구가 증가하고 있다. 특히 해상에서는 선박의 운동에 의해 크레인에 매달린 물체가 상하 동요 (heave)와 크레인을 기준으로 좌우 동요 (sway)가 발생하는데, 이러한 운동은 작업을 지연시키고, 정확한 위치에 물체를 놓지 못하게 하며, 자칫 주변 구조물과의 충돌을 야기할 수 있다. 이와 같은 동요를 최소화하는 Anti-Motion Control (AMC) 시스템은 Anti-Heave Control (AHC)과 Anti-Sway Control (ASC)을 포함한다. 본 연구에서는 해양 작업 지원선에 적합한 AMC 시스템의 설계 및 검증 방법을 연구하였다. 먼저 상하 동요를 최소화하기 위해 크레인의 와이어 길이를 능동적으로 조정하는 AHC 시스템을 설계하였다. 또한, 기존의 제어 시스템의 검증 방법은 실제 선박이나 해양 구조물에 해당 제어 시스템을 직접 설치하기 전에는 그 성능을 테스트하기가 힘들었다. 이를 해결하기 위해 본 연구에서는 Hardware-In-the-Loop Simulation (HILS) 기법을 활용하여 AHC 시스템의 검증 방법을 연구하였다. 또한, ASC 시스템을 설계할 때 제어 대상이 under-actuated 시스템이기 때문에 제어하기가 매우 어렵다. 따라서 본 연구에서는 sliding mode control 알고리즘을 이용하며 다관절 크레인 (knuckle boom crane)의 관절 (joint) 각도를 제어하여 좌우 동요를 줄일 수 있는 ASC 시스템을 설계하였다.Chapter 1 Introduction 1 1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . 1 1.2 Requirements for Autonomous Operation . . . . . . . . . . . . . 5 1.2.1 Path Following for Autonomous Ship . . . . . . . . . . . . 5 1.2.2 Collision Avoidance for Autonomous Ship . . . . . . . . . 5 1.2.3 Anti-Motion Control System for Autonomous Ship . . . . 6 1.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Related Work for Path Following System . . . . . . . . . 9 1.3.2 Related Work for Collision Avoidance System . . . . . . . 9 1.3.3 Related Work for Anti-Heave Control System . . . . . . . 13 1.3.4 Related Work for Anti-Sway Control System . . . . . . . 14 1.4 Configuration of Simulation Framework . . . . . . . . . . . . . . 16 1.4.1 Application Layer . . . . . . . . . . . . . . . . . . . . . . 16 1.4.2 Autonomous Ship Design Layer . . . . . . . . . . . . . . . 17 1.4.3 General Technique Layer . . . . . . . . . . . . . . . . . . 17 1.5 Contributions (Originality) . . . . . . . . . . . . . . . . . . . . . 19 Chapter 2 Theoretical Backgrounds 20 2.1 Maneuvering Model for Autonomous Ship . . . . . . . . . . . . . 20 2.1.1 Kinematic Equation for Autonomous Ship . . . . . . . . . 20 2.1.2 Kinetic Equation for Autonomous Ship . . . . . . . . . . 21 2.2 Multibody Dynamics Model for Knuckle Boom Crane of Autonomous Ship. . . 25 2.2.1 Embedding Techniques . . . . . . . . . . . . . . . . . . . . 25 2.3 Control System Design . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.1 Proportional-Integral-Derivative (PID) Control . . . . . . 31 2.3.2 Sliding Mode Control . . . . . . . . . . . . . . . . . . . . 31 2.4 Deep Reinforcement Learning Algorithm . . . . . . . . . . . . . . 34 2.4.1 Value Based Learning Method . . . . . . . . . . . . . . . 36 2.4.2 Policy Based Learning Method . . . . . . . . . . . . . . . 37 2.4.3 Actor-Critic Method . . . . . . . . . . . . . . . . . . . . . 41 2.5 Hardware-in-the-Loop Simulation . . . . . . . . . . . . . . . . . . 43 2.5.1 Integrated Simulation Method . . . . . . . . . . . . . . . 43 Chapter 3 Path Following Method for Autonomous OSV 46 3.1 Guidance System . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.1 Line-of-sight Guidance System . . . . . . . . . . . . . . . 46 3.2 Deep Reinforcement Learning for Path Following System . . . . . 50 3.2.1 Deep Reinforcement Learning Setup . . . . . . . . . . . . 50 3.2.2 Neural Network Architecture . . . . . . . . . . . . . . . . 56 3.2.3 Training Process . . . . . . . . . . . . . . . . . . . . . . . 58 3.3 Implementation and Simulation Result . . . . . . . . . . . . . . . 62 3.3.1 Implementation for Path Following System . . . . . . . . 62 3.3.2 Simulation Result . . . . . . . . . . . . . . . . . . . . . . 65 3.4 Comparison Results . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.4.1 Comparison Result of PPO with PID . . . . . . . . . . . 83 3.4.2 Comparison Result of PPO with Deep Q-Network (DQN) 87 Chapter 4 Collision Avoidance Method for Autonomous OSV 89 4.1 Deep Reinforcement Learning for Collision Avoidance System . . 89 4.1.1 Deep Reinforcement Learning Setup . . . . . . . . . . . . 89 4.1.2 Neural Network Architecture . . . . . . . . . . . . . . . . 93 4.1.3 Training Process . . . . . . . . . . . . . . . . . . . . . . . 94 4.2 Implementation and Simulation Result . . . . . . . . . . . . . . . 95 4.2.1 Implementation for Collision Avoidance System . . . . . . 95 4.2.2 Simulation Result . . . . . . . . . . . . . . . . . . . . . . 100 4.3 Implementation and Simulation Result for Multi-ship Collision Avoidance Method . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.3.1 Limitations of Multi-ship Collision Avoidance Method - 1 107 4.3.2 Limitations of Multi-ship Collision Avoidance Method - 2 108 4.3.3 Implementation of Multi-ship Collision Avoidance Method 110 4.3.4 Simulation Result of Multi-ship Collision Avoidance Method 118 Chapter 5 Anti-Motion Control Method for Knuckle Boom Crane 129 5.1 Configuration of HILS for Anti-Heave Control System . . . . . . 129 5.1.1 Virtual Mechanical System . . . . . . . . . . . . . . . . . 132 5.1.2 Virtual Sensor and Actuator . . . . . . . . . . . . . . . . 138 5.1.3 Control System Design . . . . . . . . . . . . . . . . . . . . 141 5.1.4 Integrated Simulation Interface . . . . . . . . . . . . . . . 142 5.2 Implementation and Simulation Result of HILS for Anti-Heave Control System . . . . . . . . 145 5.2.1 Implementation of HILS for Anti-Heave Control System . 145 5.2.2 Simulation Result of HILS for Anti-Heave Control System 146 5.3 Validation of HILS for Anti-Heave Control System . . . . . . . . 159 5.3.1 Hardware Setup . . . . . . . . . . . . . . . . . . . . . . . 159 5.3.2 Comparison Result . . . . . . . . . . . . . . . . . . . . . . 161 5.4 Configuration of Anti-Sway Control System . . . . . . . . . . . . 162 5.4.1 Mechanical System for Knuckle Boom Crane . . . . . . . 162 5.4.2 Anti-Sway Control System Design . . . . . . . . . . . . . 165 5.4.3 Implementation and Simulation Result of Anti-Sway Control . . . . . . . . . . . . . . 168 Chapter 6 Conclusions and Future Works 176 Bibliography 178 Chapter A Appendix 186 국문초록 188Docto

Comparison of Lift Path Planning Algorithms for Mobile Crane Operations in Heavy Industrial Projects

Heavy industrial projects, especially oil refineries, are constructed by modules prefabricated in factories, transported to sites and installed by mobile cranes. Due to a large number of lifts on the congested and dynamic site layouts in heavy industrial projects, the lift path planning has been attention for not only safe and efficient mobile crane operation but also better project productivity and safety. Although the path planning algorithms have been introduced over the years, they have not been used actively in practice since the comparison of these algorithms has not been examined yet based on the realistic mobility of mobile cranes and real site environment. Therefore, this thesis compares the path planning algorithms including A* search, rapidly exploring random tree (RRT), genetic algorithms (GA) and 3D visualization-based mathematical algorithm (3DVMA) under the same site environment in order to find a competent method using measurement metrics considering collision-free and optimal lift paths with the lower crane operation cost and less computation time. The proposed comparison is implemented in a case study that includes a series of modules lifted by a mobile crane on various site conditions. This comparison shows the advantages and disadvantages of each algorithm for the crane path planning in heavy industrial projects and suggests the direction of further research in this field