A recent trend in the development of off-highway construction equipment, such as excavators, is to use a system model for model-based system design in a virtual environment. Also, control system design for advanced excavation systems, such as automatic excavators and hybrid excavators, requires system models in order to design and simulate the control systems. Therefore, modeling of an excavator is an important first step toward the development of advanced excavators. This paper reviews results of recent studies on the modeling of mechanical and hydraulic subsystems for the simulation, design, and control development of excavator systems. Kinematic and dynamic modeling efforts are reviewed first. Then, various approaches in the hydraulic system modeling are presented.

The model-based system design approach allows for an efficient way of designing and developing complex engineering systems in a virtual environment [

Hydraulic excavators are from the most widely used earthmoving equipment in construction and mining industry, and they will continue to play an important role among off-highway vehicles in years to come [

The model-based system design approach can be applied to the design and development of advanced excavators, such as automatic excavators and hybrid excavators. Like any model-based system design, the usual practice in controller development for an advanced excavator system is to derive the system model first and then develop a controller based on the model. Therefore, deriving a system model is a critical component in the development of an excavator. Among many subsystems and components in an excavator, this paper is aimed at providing an overview on the recent development of system models for excavator manipulators.

An excavator manipulator is comprised of kinematically operating mechanical links and a hydraulic system. There exist two main approaches in modeling the mechanical and hydraulic systems: mathematical modeling and simulation modeling using commercially available software tools. This paper starts with a review on kinematic and dynamic modeling of the mechanical linkage, and, then, various modeling approaches on hydraulic systems will be presented. In each system modeling review, mathematical models will be presented first and then simulation models will follow.

Kinematic and dynamic models are used for simulation and controller development for an excavator manipulator system [

Kinematic equations describe the motion of an excavator manipulator without consideration of the driving forces and torques [

Excavator coordinate systems in Denavit-Hartenberg convention.

Forward kinematic equations were derived to calculate the positions and orientations of the manipulator links when the joint angles and lengths of the links are given [

Conversely, inverse kinematic relations can be employed to determine the joint angles and cylinder lengths when the positions and orientations of the links are known [

Basic behavior module of integrated behavior-based control framework.

In the kinematic design of an automatic excavator, path planning is of primary concern where the desired global coordinates of the bucket tip and the associated motion of the other links need to be determined. As an analytical method, the Cartesian-Space trajectory planning method has been extensively applied in the literature [

Although the 3rd-order method is simple to use, the major disadvantage of this approach is that the acceleration of the manipulator links is not continuous. The discontinuities in the acceleration profile may cause sudden and large force variations, which lead to jerk on the manipulator [

In addition to the analytical methods, there exist the so-called rule-based path planning methods. Yamamoto et al. and Yoshida et al. conducted a series of experiments to measure trajectories of a manipulator controlled by different operators [

Example of rule script for truck loading [

Situation | Command | |
---|---|---|

Joint 1: swing | ( | |

( | | |

( | | |

( | N/A | |

| ||

Joint 2: boom | ( | |

( | | |

| ||

Joint 3: stick | ( | |

( | | |

( | | |

( | | |

| ||

Joint 4: bucket | ( | |

( | | |

( | |

The human dependency of the produced trajectories will introduce variations inevitably. Figure

Tracks of the tips of the boom, arm, and bucket [

Experiment case 1, far operator 2, 5th trial, 1 cycle

Experiment case 3, medium operator 2, 3rd trial, 1 cycle

Experiment case 2, near operator 2, 5th trial, 1 cycle

To enhance the tracking capability for a valid path for the manipulator, a rapidly exploring random tree method was developed by Maeda et al. which improved the responses to the environment disturbances [

Example trajectory obtained by using random tree method for a path searching problem to avoid obstacles [

Another method to generate a working path was developed by Makkonen et al. by combining manipulator position data with a working zone terrain CAD model, which employs triangular elements defined by vertices [

Example trajectories created by using VMC method [

Obstacle avoidance motion

Digging motion

Recently, artificial neural networks were applied in the trajectory planning. In the research by Atmeh and Subbarao [

Additionally, a trajectory compensation method based on path prediction was developed. Using this method, a trajectory can be predicted and compensated based on real-time simulation of a simplified system model, to improve control accuracy [

In a conventional study of manipulator dynamics, mathematical models are derived by applying Newton-Euler’s or Euler-Lagrange’s method. These two different approaches are equivalent and lead to the same set of dynamic equations [

In addition to the conventional mathematical modeling, modeling methods based on transfer functions have been developed. In the research by Gu et al. [

Comparison of estimated transfer function model outputs with experimentally measured data [

In research by Tafazoli et al. [

Configuration for joint torque equations.

In their research, load pins were used to measure load torques on the links indirectly. Then, a series of static experiments without load on the bucket were carried out. In this manner, the parameters could be estimated with a 5% error [

For accurate simulation and visual presentation of excavator manipulators, various commercial software tools have been utilized. Among many choices, three software tools are widely used for excavator simulation: MATLAB/Simulink, Amesim, and Adams [

Excavator manipulator model developed in SimMechanics [

Excavator model in Adams [

Dynamic system simulation software typically has the functionality to produce dynamic properties of a manipulator when a CAD model for the manipulator is available [

For excavator manipulators, the drive forces or torques are produced by hydraulic systems including pumps, valves, and cylinders [

Hydraulic system modeling and simulation process.

The conventional modeling approach for a hydraulic system is to apply Newton’s law. For example, the following state variable vector can be defined for a simplified hydraulic system shown in Figure

Schematic of a hydraulic cylinder and control valve.

Mathematical modeling of hydraulic pipes used in manipulators has been well studied and can be found in textbooks [

In addition to mathematical modeling, excavator hydraulic systems have been modeled by using software tools, such as SimHydraulics and Amesim. In recent publications, various hydraulic system modeling software tools have been applied to model hydraulic systems [

Hydraulic system model developed in SimHydraulics [

Lee and Chang proposed a bond-graph based hydraulic system modeling approach as shown in Figure

Bond-graph model for hydraulic circuit in excavator manipulator [

It was found that friction in an excavator hydraulic system is significant and cannot be neglected [

Gray-box model of an integrated hydraulic pump system.

There have also been efforts to develop empirical models. Possible losses in hydraulic systems were also accounted in input-output relations in the gray-box approach [

In most hydraulic system modeling approaches, governing equations are derived first. Then, a graphical diagram is formed to construct a system model with hydraulic system modeling software. Additionally, the system uncertainties are estimated and bounded and then added to the system model. In this manner, a relatively accurate hydraulic system model can be developed.

Finally, some of the key features of widely used modeling and simulation software are summarized in Table

Key features of the different modeling software.

Software | Key features |
---|---|

Amesim by Simens PLM | (i) Open libraries available based on physics and applications |

| |

Adams by MSC Software | (i) Creation or import of component geometry in wireframe or 3D solids |

| |

Simscape by MathWorks | (i) Single environment for simulating multidomain physical systems with control algorithms in Simulink |

Model-based system design practice can be applied to the design and development of advanced excavators. Since the first important step in the model-based system design is the system model development, significant amount of research has been conducted on the modeling of excavator systems, especially manipulators.

The Denavit-Hartenberg process has been extensively applied in the kinematic analyses of excavator manipulators, and both experimental and analytical trajectory planning methods have been used to generate desired trajectories of excavator manipulators. Dynamic system models have been derived by applying Newton-Euler’s method or by using software tools such as SimScape, Amesim, and Adams. Hydraulic system models are usually simplified greatly due to the complexity of the real hydraulic systems. For hydraulic systems, modeling of the hydraulic loss is essential for simulation accuracy. Since it is difficult to accurately model hydraulic systems especially when the system is complex, however, designers rely mostly on commercial software tools for that purpose.

Advancement in excavator systems design can occur in many different ways. Two notable directions include electrification and hybridization for energy efficiency and automation of excavator operations. Due to the increasing complexity in the system architecture, development of these advanced excavator systems inevitably requires model-based system design approach. Therefore, accurate model development will be increasingly important and high-fidelity multiphysics software tools will be required to design and simulate both mechanical and hydraulic subsystems simultaneously.

The current state-of-the-art simulation software allows high-fidelity simulation of hydraulic systems in connection with mechanical multibody dynamics. They allow formation of complex hydraulic systems using numerous built-in component models including pipes, valves, and pumps. Using thus-formed system models, various dynamic and hydraulic performances can be simulated and studied. The simulation results are accurate enough to replace numerous physical prototyping and testing required for new system development.

While the current simulation models and software are focused mainly on the mechanical and hydraulic performances, the future research needs to be directed toward development of more energy-efficient systems by incorporating power sources and transmission. Thus, a high-fidelity internal combustion engine or hybrid electric system model needs to be employed and drive-cycle simulations need to be conducted to improve the system design for better energy efficiency.

The authors declare that they have no competing interests.