Energy-Optimal Offline Global Motion Planning of Omnidirectional Robots

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Chapter 2. Literature Review

In this chapter, the most relevant literature is reviewed and summarized. The key topics include the Mecanum wheel, the Mecanum robot design, the current state of the art of the autonomous navigation system, existing energy consumption modelling technique and existing energyefficient motion planning methods.

 Mecanum Wheel and Four-Wheeled Mecanum Mobile Robot

This section focuses on the introduction of the Mecanum wheel. It starts with background information about omnidirectional wheels. Then applications, drawbacks, kinematics, dynamics and control methods of the Mecanum wheel are properly described.

Omnidirectional Wheel Applications

Omnidirectional manoeuvrability is an outstanding ability for mobile robots to conveniently transport in congested, confined and highly dynamic environments. Mobile platforms need a good manoeuvrability to conveniently move in tight spaces and easily dodge obstacles. The locomotion design for a mobile robot is mainly selected by its working environment. The conventional wheel is an extremely popular locomotion mechanism because it is efficient, stable and easy to implement.
This makes omnidirectional wheels very useful because they provide a complete manoeuvrability that conventional wheels do not [4]. Without non-holonomic constraints, the motion trajectories of omnidirectional mobile platforms are no longer exclusive to straight trajectories and limited types of curved trajectories. Omnidirectional motions such as crab-like sideway motions, diagonal motions and spin-in-place motions can be exclusively performed by the omnidirectional mobile drive. These omnidirectional motions can effectively simplify the non-holonomic motion trajectories, e.g. the sideways motion is a one-step approach to overcome the excessive parallel parking procedures that may be the only option for differential drive platforms in certain situations. Limited by non-holonomic constraints, nonholonomic mobile platforms only follow straight-line paths and curved-line paths and have to orient their noses toward tangent directions of the path. The omnidirectional mobile drive is able to move instantaneously in any direction from any orientation. Basically, the omnidirectional drive can follow any shape of path. The effectiveness of the omnidirectional motion is superior to robotics.
The operating space is limited in many working environments, and the following omnidirectional mobile platforms/robots are applied. For example, Airtrax omnidirectional forklifts are used in warehouses; KUKA omnidirectional mobile platforms are found in the factory workshops; omnidirectional wheelchairs are used in hospitals and omnidirectional mobile robots were designed to attend the Robot Soccer World Cup RoboCup.

Omnidirectional Wheel Designs

According to the detailed studies of [5], there are two categories of omnidirectional drives: conventional omnidirectional wheel designs and special omnidirectional wheel designs. The conventional designs include active caster wheels and steered wheels. The special designs include the universal omni wheel and the Mecanum wheel. An overview is given in Table I to list the main advantages and disadvantages of each design.
Table I Advantages and Disadvantages of Omnidirectional Wheel Designs The special designs tend to utilize additional free-rolling rollers, which are attached to each wheel. These rollers alternately contact the ground, and this causes discontinuous wheelground contact. But both as special design, the Omni wheel and the Mecanum wheel are simple to control and operate for omnidirectional motions. In particular, a steering system is not necessary to both drives. The Mecanum wheel has a more complex mechanical design and is more taxing to manufacture. In return, the Mecanum wheel is more suitable to take heavy-duty tasks than the Omni wheel.

 Ilon Mecanum Wheel

The Ilon Mecanum wheel is now one of the most practical omnidirectional wheel designs in industry [6]. The Mecanum wheel was invented in 1972-1973 by Swedish engineer and inventor Bengt Erland Ilon. The wheel is named after the Swedish company Mecanum AB, where he was working when he invented it. Its patent was then bought by the US Navy in 1975 and used to design different scales of the mobile platforms for military purposes [7]. The Mecanum wheel, shown in Figure 1, is a near round-shaped wheel, which has an actively rotating hub (silver colour in Figure 1) with a certain number of passively rolling rollers (black rubber colour in Figure 1) mounted around the wheel circumference at an angle – conventionally, that angle is 45°. The geometry of the roller is a specially designed curvature so that the curved geometry makes the overall shape of the Mecanum wheel remain circular from the side view of the Mecanum wheel. More information about the geometry design of the rollers can be found in [8].
Figure 1 The Mecanum wheel used on the designed robot in this project. This heavy-duty Mecanum wheel has 7 rollers mounted around the wheel circumference. Each roller is attached to the wheel at both sides of the roller. The wheel has a weight of 8 kg, a radius of 0.11 m and a width of 0.15 m.

Omnidirectional Motions of the Mecanum Drive

Just as the conventional car wheel operates, the Mecanum wheel is rotated by active motor torque on the ground and a driving force is generated between the ground and the wheel due to the ground static friction. But the angled roller that is in contact with the ground, generates an angled driving force acting on the Mecanum wheel with respect to the ground. A Mecanum drive consists of most commonly four Mecanum wheels, or sometimes more for heavy-duty applications. Because each Mecanum wheel is independently controlled by an individual motor, the angled driving forces of the Mecanum wheels can be in opposite directions along the rotation axis of the rollers and have different amounts of magnitudes. The combination of every angled driving force from each Mecanum wheel can be in any direction [9]. The direction of the combined force can be controlled only by the velocities of the Mecanum wheel so the Mecanum robot is capable of omni-directional motion without wheel steering. Motion is achieved merely by implementing different velocity combinations of the Mecanum wheels, asshown in Figure 2. Simply controlling the rotations of each Mecanum wheel without any complex steering system can easily operate, manage and control the omnidirectional motions of the drive.
Figure 2 Combinational wheel actuations for general motion [10]. There are two types of the Mecanum wheel design, distinguished by the way the rollers are attached to the wheel hub. The first type attaches the roller to the hub at the centre of the roller, as shown in Figure 3. This type of roller is easily manufactured at low cost, and it is usually used as the kits of small-scale robots. The second type of Mecanum wheel supports the roller from both sides of the roller, as shown in Figure 1. This second type tends to have much better loading capability than the first type.
Compared with other omnidirectional wheels, the Mecanum wheel is a lot more suitable for taking heavy-duty tasks. This is the critical reason why the Mecanum wheel has much wider practical applications, especially in industry, than any other omnidirectional wheel. These days, most of the heavy-duty Mecanum wheels utilized in industry belong to the second type. Figure 3 The Mecanum wheel from CAD. The roller attachment is at the centre of the roller.
In order to have a Mecanum drive properly working, there are must be two kinds of the Mecanum wheels on the Mecanum platform. As shown in Figure 2, the orientations of the rollers of the Mecanum wheels can be categorized into two kinds, which are distinguished by the orientation of the roller arrangement. Using the Mecanum wheel in Figure 3 as an example, the roller that is in contact with the ground is oriented like Figure 4 (a), if viewing the Mecanum wheel from above.Thus, there are two ways to organize the Mecanum wheel on the Mecanum robot and both ways are able to have the Mecanum drive working properly, as shown in Figure 5. The wheel arrangement in Figure 5 (a) is named an ‘O’ arrangement and the wheel arrangement in Figure 5 (b) is named an ‘X’ arrangement, in this thesis.
The illustrated thread of the roller is the one that is in contact with the ground, viewed from above. It is worth mentioning that, it is very important to clarify which roller is illustrated in the figures. This is because the roller on the top of the Mecanum wheel has exactly the opposite orientation to the roller contacting with the ground, on the same Mecanum wheel. Otherwise, this may cause much confusion. The Mecanum robot in this PhD project utilizes the ‘O’ wheel arrangement of Figure 5 (a).
(a) ‘O’ arrangement (b) ‘X’ arrangement Figure 5 ‘O’ and ‘X’ wheel arrangements on working Mecanum robots.
The ‘O’ wheel arrangement of Figure 5 (a) is also shown in the CAD model of Figure 6 below for better illustration purposes. Viewing Figure 6 (b) from above, the roller arrangement seems to be ‘X’ in Figure 5 (b). But it is important to remember that the roller on the top of the Mecanum wheel has exactly the opposite orientation to the roller contacting with the ground, on the same Mecanum wheel. Thus, the roller that is in contact with ground in Figure 6 (b) is ‘O’ as in Figure 5 (a).

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Chapter 1. Introduction
1.1. Background
1.2. Project Aim and Objectives
1.3. Structure of the Thesis
Chapter 2. Literature Review
2.1. Mecanum Wheel and Four-Wheeled Mecanum Mobile Robot
2.2. Mechatronics Design of a Heavy-Duty Autonomous Omnidirectional Mecanum Robot
2.3. State of the Art of Autonomous Navigation
2.4. Dynamic Window Approach
2.5. Energy Consumption Model
2.6. Energy Efficient Motion Planning
2.7. Summary
Chapter 3. Mechatronics Design of a Heavy-Duty Omnidirectional Mecanum Robot
3.1. Introduction
3.2. Overview
3.3. Electromechanics
3.4. Locomotion Control System
3.5. Autonomous Navigation System
3.6. Control System Architecture
3.7. Closed-Loop Motion Control
3.8. Implementation
3.9. Virtual Simulation
3.10. Operation Instructions and Maintenance
3.11. Summary
Chapter 4. Energy Consumption Model of the Four-Wheeled Omnidirectional Mecanum Robot
4.1. Introduction
4.2. Dynamics Model of Four-Wheeled Omnidirectional Mecanum Robot
4.3. Energy Consumption Model
4.4. Implementation
4.5. Verification
4.6. Summary
Chapter 5. Energy-Optimal Online Local Trajectory Planning for Autonomous Navigation
5.1. Introduction
5.2. Methodology
5.3. Extended Dynamic Window Approach
5.4. Implementation
5.5. Experimental Verification
5.6. Summary
Chapter 6. Energy-Optimal Offline Global Motion Planning of Omnidirectional Robots
6.1. Introduction
6.2. Methodology – Energy-Optimal Polynomial Trajectory Generation
6.3. Energy-Optimal Global Motion Planning
6.4. Implementation
6.5. Verification
6.6. Summary
Chapter 7. Conclusion and Future Work
7.1. Contributions
7.2. Conclusions
7.3. Future Work
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Mechatronics Design and Energy-Efficient Navigation of a Heavy-Duty Omni-Directional Mecanum Autonomous Mobile Robot Li

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