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Chassis and Locomotion Mechanisms

Introduction

The chassis is the mobile platform of a robot. The choice of locomotion mechanism directly determines the robot's motion capabilities, terrain adaptability, and control complexity. This section covers common wheeled locomotion mechanisms and their kinematic models.

Differential Drive

Differential drive is the simplest and most common wheeled locomotion mechanism, consisting of two independently driven wheels plus one or more passive support wheels (caster/ball).

Structure

    [Left wheel vL]  ---[Chassis]---  [Right wheel vR]
                         |
                    [Caster (passive)]

Kinematic Model

Let the left and right wheel velocities be \(v_L\) and \(v_R\), with wheel spacing \(L\) (track width):

Linear velocity (robot center):

\[v = \frac{v_R + v_L}{2}\]

Angular velocity:

\[\omega = \frac{v_R - v_L}{L}\]

Inverse kinematics (solving wheel speeds from desired velocities):

\[v_R = v + \frac{\omega L}{2}\]
\[v_L = v - \frac{\omega L}{2}\]

Motion Types

Motion Condition Description
Straight \(v_L = v_R\) Both wheels same speed
Spin in place \(v_L = -v_R\) Wheels opposite and equal speed
Arc \(v_L \neq v_R\), same sign Turns toward the slower wheel
Single-wheel pivot \(v_L = 0\) or \(v_R = 0\) Rotates about the stationary wheel

Turning Radius

\[R = \frac{L}{2} \cdot \frac{v_R + v_L}{v_R - v_L}\]

When \(v_R = -v_L\), \(R = 0\) (spin in place).

Pose Update (Odometry)

Discrete time step \(\Delta t\):

\[\begin{aligned} x_{k+1} &= x_k + v \cdot \cos(\theta_k) \cdot \Delta t \\ y_{k+1} &= y_k + v \cdot \sin(\theta_k) \cdot \Delta t \\ \theta_{k+1} &= \theta_k + \omega \cdot \Delta t \end{aligned}\]

Pros and Cons

  • Pros: Simple structure, intuitive control, can spin in place, low cost
  • Cons: Cannot move laterally (non-holonomic constraint), caster may vibrate on uneven ground
  • Applications: TurtleBot, robot vacuums, many ROS educational robots

Omnidirectional Wheels

Mecanum Wheel

Mecanum wheels have 45°-angled rollers on the rim. Through the speed combination of 4 wheels, omnidirectional motion is achieved.

4-Wheel Mecanum Kinematics:

Let the four wheel speeds be \(v_1, v_2, v_3, v_4\) (front-left, front-right, rear-left, rear-right), with track width \(L\) and wheelbase \(W\):

\[v_x = \frac{v_1 + v_2 + v_3 + v_4}{4}\]
\[v_y = \frac{-v_1 + v_2 + v_3 - v_4}{4}\]
\[\omega = \frac{-v_1 + v_2 - v_3 + v_4}{4(L + W)}\]

Inverse Kinematics:

\[\begin{aligned} v_1 &= v_x - v_y - (L+W)\omega \\ v_2 &= v_x + v_y + (L+W)\omega \\ v_3 &= v_x + v_y - (L+W)\omega \\ v_4 &= v_x - v_y + (L+W)\omega \end{aligned}\]

Motion Modes:

Motion Wheel Speed Configuration
Forward All four wheels same speed, same direction
Lateral Diagonal wheels same direction, adjacent wheels opposite
Spin in place Left-side and right-side wheels opposite
Diagonal Specific wheel speed combinations

Omni Wheel

Omni wheels have free rollers perpendicular to the wheel axis, commonly used in 3-wheel 120° layouts.

3-Wheel Omni Kinematics:

\[\begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix} = \begin{bmatrix} -\sin\alpha_1 & \cos\alpha_1 & R \\ -\sin\alpha_2 & \cos\alpha_2 & R \\ -\sin\alpha_3 & \cos\alpha_3 & R \end{bmatrix} \begin{bmatrix} v_x \\ v_y \\ \omega \end{bmatrix}\]

Where \(\alpha_i\) is the mounting angle of each wheel (120° intervals), and \(R\) is the distance from wheel to center.

Mecanum vs. Omni

Feature Mecanum (4-wheel) Omni (3-wheel) Omni (4-wheel)
Omnidirectional motion Yes Yes Yes
Load capacity High Medium-low Medium
Control complexity Medium Medium Medium
Ground requirement Flat Flat Flat
Efficiency Medium (45° roller losses) High High
Cost Higher Medium Medium
Applications RoboMaster, AGV Soccer robots Indoor logistics

Ackermann Steering

Ackermann steering is the common steering mechanism used in automobiles, with front-wheel steering and rear-wheel drive.

Kinematic Model

Let the front wheel steering angle be \(\delta\), wheelbase (front-to-rear axle distance) be \(L_{wb}\), and rear wheel speed be \(v\):

Turning Radius:

\[R = \frac{L_{wb}}{\tan\delta}\]

Angular Velocity:

\[\omega = \frac{v}{R} = \frac{v \cdot \tan\delta}{L_{wb}}\]

Pose Update:

\[\begin{aligned} \dot{x} &= v \cos\theta \\ \dot{y} &= v \sin\theta \\ \dot{\theta} &= \frac{v \tan\delta}{L_{wb}} \end{aligned}\]

Ackermann Geometry

Inner and outer wheel steering angles differ to avoid tire side-slip:

\[\cot\delta_o - \cot\delta_i = \frac{W}{L_{wb}}\]

Where \(\delta_o\) is the outer wheel angle, \(\delta_i\) is the inner wheel angle, and \(W\) is the track width.

Pros and Cons

  • Pros: Good high-speed stability, low tire wear, can carry heavy loads
  • Cons: Has minimum turning radius, cannot spin in place, complex structure
  • Applications: Autonomous vehicles, high-speed outdoor robots

Tracked (Skid-Steer)

Kinematics

Tracked vehicle kinematics are similar to differential drive, with steering achieved by varying left and right track speeds:

\[v = \frac{v_R + v_L}{2}, \quad \omega = \frac{v_R - v_L}{B}\]

Where \(B\) is the center-to-center distance between tracks.

Characteristics

  • Pros: Strong off-road capability, large ground contact area, slip-resistant, can cross obstacles
  • Cons: Low efficiency (track side-slip during turning), high wear, noisy, slow
  • Applications: Bomb disposal robots, field exploration, military robots

Locomotion Mechanism Comparison

Feature Differential Drive Mecanum Omni Ackermann Tracked
Omnidirectional No Yes No No
Spin in place Yes Yes No Yes
High-speed stability Medium Low High Medium
Off-road capability Low Very low Medium High
Load capacity Medium High High High
Control complexity Low Medium Medium Low
Mechanical complexity Low Medium High Medium
Cost Low Medium-high Medium Medium
Typical applications Service robots Indoor logistics Autonomous driving Field exploration

Selection Decision Flow

graph TD
    A[Application Scenario] --> B{Lateral movement needed?}
    B -->|Yes| C[Mecanum / Omni Omnidirectional]
    B -->|No| D{Complex terrain?}
    D -->|Yes| E[Tracked]
    D -->|No| F{High speed needed?}
    F -->|Yes| G[Ackermann Steering]
    F -->|No| H{Spin in place needed?}
    H -->|Yes| I[Differential Drive]
    H -->|No| G

Wheels and Tires

Wheel Types

Type Diameter Range Features Suitable For
Rubber wheel 30–300 mm Good grip, shock absorption General
Omni wheel 40–100 mm Free lateral movement Omni chassis
Mecanum wheel 60–200 mm 45° rollers Omni chassis
Pneumatic tire 100–400 mm Good shock absorption Outdoor
Hard wheel (nylon/POM) 30–100 mm Low resistance, wear-resistant Smooth floors

Wheel Size Selection

  • Speed vs. wheel diameter relationship: \(v = \omega_{wheel} \times r\)
  • Large wheels: Higher speed, better obstacle crossing, but higher torque demand
  • Small wheels: Lower torque demand, compact, but poor obstacle crossing

Chassis Structural Design

Material Selection

Material Manufacturing Method Strength Weight Cost Suitable Stage
Acrylic sheet Laser cutting Low Light Low Prototype / education
3 mm aluminum plate Laser / CNC Medium Medium Medium Prototype
Carbon fiber plate CNC High Very light High Competition / product
3D printed (PLA) FDM Low-medium Medium Low Rapid prototype
Sheet metal Bending Medium-high Medium Medium Production

Chassis Design Guidelines

  1. Keep center of gravity low: Place battery at the bottom
  2. Rigid motor mounting: Prevent deformation that causes gear misalignment
  3. Cable routing space: Reserve adequate cable channels
  4. Modular mounting: Use standard hole patterns for sensors and circuit boards
  5. Maintainability: Easy disassembly and servicing

References

  • Siegwart & Nourbakhsh: "Introduction to Autonomous Mobile Robots"
  • ROS Navigation Stack: Chassis kinematics interfaces
  • RoboMaster open-source chassis designs

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