Kinematics & Comparison of a Mobile robot wheels

mobile robot wheel kinematics

1. Comparison between Conventional & Mecanum Wheels VS Overview of wheel types in robotics. Design features, mechanics, and movement principles.

2. 1. Design & Motion & Kinematics conventional Design : Solid or pneumatic circular wheels without rollers. Motion : Designed for straightforward forward/backward motion. Rotational motion is achieved using a differential drive system or steering mechanisms Kinematics : Simple; relies on linear and angular velocities derived directly from wheel rotations. 2 or 4 independent drive motors Mecanum Design : Wheels equipped with angled rollers (typically 45° or 60°) around the rim. Motion : Allows omnidirectional movement, including forward, backward, sideways, and rotation without changing the robot's orientation. Kinematics : More complex; requiring advanced control algorithms for precise movement. As it requires understanding force vectors and projecting motion based on roller geometry.

3. 2. Friction Analysis conventional Static and Dynamic Friction : Frictional force is given by: where: : Coefficient of friction : Normal force acting on the wheel Frictional Forces: Primarily along the direction of motion; turning friction adds complexity to analysis. Higher Traction : Higher due to the absence of rollers, providing strong grip on most surfaces due to higher normal contact area. Slippage : slippage is minimal in controlled environments Skidding occurs during sharp turns or abrupt braking due to lateral forces.   Mecanum Force Components : Forces on each roller split into tangential and normal components. For a roller angled at α : where: : Total force applied : Tangential force for motion : Roller-induced force Frictional Forces : Forces are distributed along the roller axes, introducing energy loss and requiring precise calibration. Lower Traction : Due to the rollers, contact area with the ground is reduced compared to conventional wheels. Slippage : More prone to slippage, especially on smooth or inclined surfaces, due to distributed forces through rollers.  

4. 3. Dynamic Analysis conventional Torque required for motion: where is the moment of inertia, and is angular acceleration. Power efficiency. Mecanum Torque losses due to rollers: Power efficiency is reduced due to energy dissipation in rollers.

5. 4. Control System Complexity & Kinematics Restrictions : conventional Control Complexity : Simple control algorithms (PID or basic control loops, basic trajectory tracking) Forward Kinematics : Straightforward; uses simple equations for motion along the x-axis and y-axis. Turning involves a differential steering model. Inverse Kinematics : Easier to calculate, primarily focused on linear velocity and angular velocity. Mecanum Control Complexity : Requires more advanced controllers. (e.g., PID with feedforward, model predictive control). Precise calibration is critical. Forward Kinematics : Complex; involves projecting forces through rollers to achieve omnidirectional motion. Inverse Kinematics : Requires matrix inversion; errors in calibration lead to significant inaccuracies.

6. 5. Wear and Tear & Energy Efficiency & Payload Distribution conventional Wear and Tear: have more uniform wear. Energy Efficiency: more efficient due to direct force transfer. Payload Distribution: handle higher loads due to better traction. Mecanum Wear and Tear: suffer from uneven roller wear. Energy Efficiency: lose energy through rollers. Payload Distribution: struggle on uneven surfaces.

7. 6. Applications and Use Cases conventional Best for outdoor environments or where straight-line motion is prioritized. Applications: Delivery robots, agricultural robots, off-road vehicles. Mecanum Ideal for indoor, smooth environments requiring high maneuverability (e.g., warehouses, factories). Applications: AGVs (Automated Guided Vehicles), service robots, robots in narrow aisles.

8. 7. Choosing the Right Option for Our Project Considering our project focuses on a Warehouse iFollow Robot: Advantages of Mecanum Wheels: Their ability to move omnidirectionally simplifies navigation in confined spaces, such as warehouse aisles. Disadvantages of Mecanum Wheels: Slippage and lower traction may reduce reliability when carrying a 30 kg load, particularly on less-than-ideal surfaces.   On the other hand, Conventional Wheels: Offer higher traction and are better suited for handling heavier payloads. May require more space for turning and might complicate path-planning algorithms in tight spaces.

9. Kinematics Derivation of Conventional & Mecanum Wheels for 4-Wheeled Mobile Robot Forward Kinematics Derivation. Inverse Kinematics Derivation.

10. First: Derivation of Conventional Wheels for 4-Wheeled Mobile Robot

11. Forawrd Kinematics     Inverse Kinematics

12. Second: Derivation of Mecanum Wheels for 4-Wheeled Mobile Robot

13. Mecanum wheel specifications

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15. Each wheel velocity decomposes into two perpendicular components due to the roller angle ( α ): Tangential velocity  : Motion parallel to the wheel axis. Roller velocity ​: Motion perpendicular to the wheel axis. Using the geometric relationship: Wheel Force Decomposition: Each Mecanum wheel's force is decomposed due to its rollers angled at  . This allows contributions to both translational and rotational motions:  

16. Forawrd Kinematics For a robot with four mecanum wheels arranged in a rectangular pattern, The contribution of each wheel to the robot's , and   is calculated considering the roller geometry.   For desired robot velocities  , and   , the wheel angular velocities are computed as:   Inverse Kinematics

17. Aspect   Conventional Wheels   Mecanum Wheels   Kinematics   - Easier to implement - Lower computation requirements   Complex; involves force decomposition - Requires calibration   Terrain Handling   - Handles uneven terrain better - More suitable for outdoor use   - Best suited for smooth, indoor surfaces   Energy Efficiency   - More energy-efficient due to fewer losses   - Energy losses in roller mechanisms    

18. Aspect   Conventional Wheels   Mecanum Wheels   Traction   - High traction on most surfaces   - Lower traction, prone to slippage   Maneuverability   - Limited to linear and rotational motion   Full omnidirectional control   Control Complexity Low complexity   High complexity   Cost Cost-effective   Expensive due to specialized design  

19. Aspect   Conventional Wheels   Mecanum Wheels   Advantages       - High efficiency - Simple control systems - High traction - Cost-effective   - Omnidirectional movement - Compact maneuverability in tight spaces - Eliminates the need for steering mechanisms   Disadvantages       - Limited to linear and rotational motion - Larger turning radii for 4-wheel setups     - Lower traction - Higher power loss due to rollers - High cost and complex control