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Overview

Work Package 1 focuses on understanding and simulating the Mecanum robot’s motion using MATLAB. Before building physical hardware, it’s essential to model the robot mathematically to:
  • Understand how wheel velocities translate to robot motion
  • Predict robot behavior for different control inputs
  • Validate designs before committing to hardware
  • Develop control algorithms in a safe, virtual environment
Duration: Suggested 4 weeks (can overlap with WP2) Prerequisites: MATLAB basics, linear algebra, trigonometry

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Learning Objectives

By the end of WP1, you will be able to:
  • ✅ Derive forward and inverse kinematics for Mecanum wheel robots
  • ✅ Implement kinematics equations in MATLAB
  • ✅ Simulate robot trajectories (linear, rotational, combined)
  • ✅ Visualize robot motion and wheel velocities
  • ✅ Analyze how robot parameters affect performance

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Deliverables

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D1.1: Kinematics of the Mecanum Robot

Suggested Time: 1 week What to deliver:
  • Mathematical derivation of kinematics equations
  • MATLAB functions for forward and inverse kinematics
  • Validation tests showing correctness
  • Documentation explaining your approach
Success Criteria:
  • Equations correctly relate wheel velocities to robot velocity
  • MATLAB code produces expected results for test cases
  • Clear explanation of coordinate frames and assumptions

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D1.2: Trajectory Planning and Visualization

Suggested Time: 3 weeks What to deliver:
  • MATLAB simulation of robot following trajectories:
    • Square path (1m × 1m) with constant orientation
    • Circular path (1m diameter) with constant orientation
    • Circular path with robot facing inward
    • Custom trajectories (your choice - be creative!)
  • Visualization showing:
    • Robot position and orientation over time
    • Individual wheel velocities
    • Path tracking error
  • Analysis of how wheel size and robot dimensions affect motion
Success Criteria:
  • Robot successfully follows planned trajectories in simulation
  • Smooth wheel velocity commands (no discontinuities)
  • Professional plots with labels, legends, and titles
  • Analysis shows understanding of parameter effects

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Why Simulation Matters

Simulation lets you test different robot dimensions (wheel size, wheelbase, track width) before building hardware. You can optimize for speed, maneuverability, or payload capacity.
Develop and test control algorithms (PID, trajectory following) in MATLAB before implementing on ESP32. Debugging in MATLAB is much faster than on hardware.
Mecanum wheels create unique motion coupling. Simulation helps visualize how each wheel contributes to overall robot motion, building intuition.
Simulate effects of wheel slippage, encoder errors, or manufacturing tolerances. Understand limitations before real-world testing.

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Mecanum Wheel Basics

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How Mecanum Wheels Work

A Mecanum wheel consists of rollers mounted at 45° to the wheel axis. When multiple Mecanum wheels work together, they enable:
  • Forward/Backward: All wheels rotate in same direction
  • Strafing (Sideways): Diagonal wheel pairs rotate in opposite directions
  • Rotation: Left and right wheels rotate in opposite directions
  • Diagonal Motion: Combination of the above
Mecanum Wheel Roller Configuration

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Coordinate Frames

Understanding coordinate frames is crucial for kinematics: Robot Frame (Body-Fixed):
  • Origin: Center of robot
  • X-axis: Forward direction
  • Y-axis: Left direction (perpendicular to X)
  • Z-axis: Upward (right-hand rule)
Global Frame (World-Fixed):
  • Fixed reference frame
  • Robot moves through this frame
  • Used for trajectory planning
Wheel Frame:
  • Each wheel has its own frame
  • Rotation axis and roller contact direction

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Robot Configuration

For this project, we use a 4-wheel Mecanum configuration: 
    Front
  ┌───────┐
  │ ①   ② │
  │       │   ① Front-left wheel
  │ ③   ④ │   ② Front-right wheel
  └───────┘   ③ Rear-left wheel
    Rear      ④ Rear-right wheel
Key Parameters:
  • L: Wheelbase (front-rear distance)
  • W: Track width (left-right distance)
  • r: Wheel radius
  • α: Roller angle (typically 45°)

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Tools and Resources

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Required Software

  • MATLAB R2020a or later (university license)
  • Toolboxes: None strictly required, but helpful:
    • Robotics System Toolbox (optional)
    • Symbolic Math Toolbox (optional for derivations)
Alternative: Octave (free, but some syntax differences)

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MATLAB Skills Needed

Programming Basics

  • Functions and scripts
  • Loops and conditionals
  • Arrays and matrices
  • Plotting (plot, subplot, xlabel, ylabel)

Mathematical Operations

  • Matrix multiplication
  • Trigonometric functions (sin, cos, atan2)
  • Numerical integration (ode45 or simple Euler)
  • Linear algebra (matrix inverse, transpose)

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Learning Resources

If you need to brush up on MATLAB:
  • MathWorks MATLAB Onramp (free 2-hour course)
  • University MATLAB tutorials (check your course portal)
  • MATLAB Documentation (excellent built-in help)
Pro Tip: Use MATLAB’s built-in documentation! Type doc functionname to get detailed help and examples.

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Project Structure

Organize your MATLAB code in a clear folder structure: 
wp1-matlab/
├── README.md                      # Project overview
├── kinematics/
│   ├── forward_kinematics.m       # Wheel vel → Robot vel
│   ├── inverse_kinematics.m       # Robot vel → Wheel vel
│   └── test_kinematics.m          # Validation tests
├── simulation/
│   ├── simulate_trajectory.m      # Main simulation function
│   ├── trajectories/
│   │   ├── square_traj.m          # Square path
│   │   ├── circle_traj.m          # Circular path
│   │   └── custom_traj.m          # Your creative trajectory
│   └── visualize_motion.m         # Plotting functions
├── parameters/
│   └── robot_params.m             # Robot dimensions, wheel size
└── results/
    ├── figures/                   # Save plots here
    └── data/                      # Save simulation data

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Getting Started Steps

1

Review Kinematics Theory

Read the Kinematics page to understand the mathematical foundation
2

Set Up MATLAB Project

Create folder structure and parameter file with your robot dimensions
3

Implement Forward Kinematics

Write function to convert wheel velocities to robot velocity
4

Implement Inverse Kinematics

Write function to convert desired robot velocity to wheel velocities
5

Test and Validate

Verify kinematics with simple test cases (forward only, strafe only, etc.)
6

Plan Trajectories

Generate time-series of desired robot positions for different paths
7

Simulate Motion

Integrate robot motion over time using kinematics and trajectory commands
8

Visualize and Analyze

Create plots showing robot path, wheel velocities, and tracking performance

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Common Approaches

Model robot as velocity-controlled system:
  • Input: Desired robot velocities (Vₓ, Vᵧ, ω)
  • Kinematics: Calculate required wheel velocities
  • Integration: Update robot pose numerically
Pros: Simple, matches hardware control Cons: Accumulates integration error in simulation

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Approach 2: Position-Level Control

Plan exact trajectory, then compute velocities:
  • Input: Desired position vs time
  • Differentiation: Calculate velocity from position
  • Kinematics: Convert to wheel velocities
Pros: Exact path following Cons: Requires smooth, differentiable trajectories

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Approach 3: Hybrid

Combine both approaches for realistic simulation:
  • High-level: Position trajectory planning
  • Low-level: Velocity control with feedback
Pros: Most realistic, shows controller effects Cons: More complex to implement

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Tips for Success

Begin with stationary robot, then forward motion, then add complexity. Don’t try to simulate everything at once!
Test kinematics with hand-calculated examples. If forward motion gives wrong velocity, fix before adding rotation.
Name variables clearly: wheel_radius not r, robot_pose not x. Your future self will thank you.
Visualize intermediate results. Plot wheel velocities, robot velocity, trajectory error. Helps debugging and understanding.
Explain what each section does. Include units in comments (e.g., % velocity in m/s).

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What to Include in Report

For your project proposal and final report, include:
  1. Kinematics Derivation:
    • Coordinate frame definitions
    • Roller geometry and force analysis
    • Matrix equations for forward and inverse kinematics
    • Assumptions and limitations
  2. MATLAB Implementation:
    • Code structure overview (don’t paste all code, just key functions)
    • Parameter values used (wheel size, robot dimensions)
    • Validation test results
  3. Simulation Results:
    • Trajectory plots (position vs time, 2D path)
    • Wheel velocity profiles
    • Analysis of results (does it match expectations?)
    • Effects of parameter changes
  4. Figures:
    • Professional quality plots with labels
    • Multiple trajectories in one figure for comparison
    • All figures numbered and referenced in text

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Next Steps

Ready to dive in? Continue with the technical pages:

Kinematics Derivation

Learn the math behind Mecanum motion

Trajectory Planning

Plan and simulate robot paths in MATLAB

Hardware Reference

Check motor specs for realistic parameters

Project Proposal

Include WP1 results in your proposal

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References

[1] K. Kanjanawanishkul, “Omnidirectional wheeled mobile robots: Wheel types and practical applications,” International Journal of Advanced Mechatronic Systems, vol. 6, no. 6, pp. 289–302, Feb. 2015. [2] M. T. Watson, D. T. Gladwin, and T. J. Prescott, “Collinear Mecanum Drive: Modeling, Analysis, Partial Feedback Linearization, and Nonlinear Control,” IEEE Transactions on Robotics, vol. 37, no. 2, pp. 642–658, Apr. 2021.