Kinematics & Comparison of a Mobile robot wheels

Kinematics & Comparison of a Mobile robot wheels

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  Comparison between Conventional& Mecanum Wheels VS  Overview of wheel types in robotics.  Design features, mechanics, and movement principles.
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  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.
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  2. Friction Analysis conventional Static and Dynamic Friction: Frictional force is given by: where: o : Coefficient of friction o : 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: o : Total force applied o : Tangential force for motion o : 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.
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  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.
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  4. Control SystemComplexity & 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.
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  5. Wear andTear & 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.
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  6. Applications andUse 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.
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  7. Choosing theRight 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.
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  Kinematics Derivation ofConventional & Mecanum Wheels for 4-Wheeled Mobile Robot  Forward Kinematics Derivation.  Inverse Kinematics Derivation.
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  First: Derivation ofConventional Wheels for 4-Wheeled Mobile Robot
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  Forawrd Kinematics InverseKinematics
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  Second: Derivation ofMecanum Wheels for 4-Wheeled Mobile Robot
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  Mecanum wheel specifications
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  Each wheel velocitydecomposes 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:
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  Forawrd Kinematics • Fora 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
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  Aspect Conventional WheelsMecanum 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
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  Aspect Conventional WheelsMecanum 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
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  Aspect Conventional WheelsMecanum 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