SLAMurai Autonomous Robot

This project is an open-source implementation of a SLAM (Simultaneous Localization and Mapping) robot.
All CAD and software is contained within this repo.

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Requirement Check

• Omnidirectional movement using 4 dual-layer omniwheels
• Report odometry accurate to 3cm at 8ft range
  • Last test: 12/20/2025 with 0.5% error in forward odom, within 3% error for side movement when moving 8ft straight. And 3cm off-center drift when doing pure diagonal.

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Features

• Real-time mapping (SLAM Toolbox)
• Autonomous navigation (Nav2)
• High-precision stepper-based odometry

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Detailed Robot Design

Payload

• 4x NEMA 17 Stepper Motors: 0.25kg each = 1.0kg total
• 4x 60mm Omni wheels: 0.1kg each = 0.4kg total
• 1x 6000mAh Lipo battery: 0.55kg
• 1x NVIDIA Jetson Xavier NX: 0.2kg
• 1x Intel RealSense D455: 0.3kg
• 3x Chassis plates: 0.3kg total
• 1x RPLIDAR A1: 0.2kg

Total weight: 3.5kg rounded

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Desired robot specs

• Speed: 0.3 m/s
• Acceleration: 0.5 m/s²
• Max payload: 3.5 kg
• Wheels: 60mm (0.0297m radius) omni wheels in 90° configuration
• Worst case surface: Concrete (Rolling resistance ~0.03)
• Torque safety factor: 2

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Selecting Motor Parameters

Required torque

$$ F_{\text{roll}} = \mu \cdot F_{\text{normal}} = 0.03 \cdot 3.5 \text{kg} \cdot 9.81 \text{m/s}^2 = 1.03 \text{N} $$

$$ F_{\text{accel}} = 3.5 \text{kg} \cdot 0.5 \text{m/s}^2 = 1.75 \text{N} $$

$$ F_{\text{total}} = 1.03 \text{N} + 1.75 \text{N} = \boxed{2.78 \text{N}} $$

$$ \tau = F_{\text{total}} \cdot r_{\text{wheel}} = 2.78 \text{N} \cdot 0.0297 \text{m} = \boxed{0.082 \text{Nm}} $$

This gives us the total torque required for the robot to meet our acceleration target. However, we need the worst-case torque per motor. One might assume it splits evenly between two motors when moving forward/backward or left/right. But could diagonal movement need more?

If each motor provides torque $T$, the top/bottom motors contribute $2T\cos(\theta)$ and left/right motors $2T\cos(90^\circ - \theta)$, where $\theta$ is the angle of travel. We can solve for $T$ to achieve some total torque $\tau$:

$$ \tau = 2T\cos(\theta) + 2T\cos(90^\circ - \theta) \implies T = \frac{\tau}{2(\cos(\theta) + \sin(\theta))} $$

$T$ peaks when $\cos(\theta) + \sin(\theta)$ is minimized. We only consider $0 \leq \theta \leq 90^\circ$ since if the angle is $> 90^\circ$, we switch the direction of the top/bottom motors, yielding an angle $0 \leq \theta \leq 90^\circ$ again. Therefore the maximum of $T$ occurs when $\theta = 0^\circ$ or $90^\circ$. So yes, the worst case is moving purely along the top/bottom or left/right axes, splitting torque evenly:

$$ T = \frac{\tau}{2} = \frac{0.082 \text{Nm}}{2} = \boxed{0.041 \text{Nm}} \cdot 2_{\text{(safety factor)}} \approx \boxed{0.082 \text{Nm worst case per motor}} $$

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Required RPM

$$ \text{RPM} = \frac{\text{Target velocity} \cdot 60}{2\pi r} = \frac{0.3 \text{m/s} \cdot 60}{2\pi \cdot 0.0297 \text{m}} \approx \boxed{96.5 \text{RPM}} $$

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Motor & Driver Selection

• NEMA 17 Stepper Motors paired with an Arduino CNC Shield
• 800 steps/rev (1/4 microstepping)

Driver:

• A4988 or DRV8825 drivers
• Up to 2A current capability

Steppers provide high holding torque and precise positioning without needing external encoders. While they don't have current sensing, the open-loop nature of steppers is offset by our odometry integration.

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Battery Selection & Longevity

• Voltage: 12V (3S Lipo)
• Desired Runtime: 1 hour

Total continuous current draw

• Motors: 0.4A each → 1.6A total
• Jetson Xavier NX: ~15W @ 12V → 1.25A
• RealSense D455: ~3.5W @ 5V → ~0.35A at 12V side
• RPLIDAR A1: ~100mA

$$ I_{\text{total}} \approx 1.6 + 1.25 + 0.35 + 0.1 = \boxed{3.3 \text{A}} $$

To run for 1 hour:

$$ \text{Capacity} = I_{\text{total}} \cdot \text{Time} = 3.3 \text{A} \cdot 1 \text{h} = 3.3 \text{Ah} = 3300 \text{mAh} $$

Our 6000mAh battery is more than sufficient, providing a significant safety margin.

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Wheel Kinematics

We use inverse kinematics to command motor speeds from a target chassis twist and forward kinematics to compute odometry.

Inverse Kinematics

$$ \begin{aligned} \begin{bmatrix} \omega_1\\ \omega_2\\ \omega_3\\ \omega_4 \end{bmatrix} &= \frac{1}{r} \begin{bmatrix} \sin(\gamma) & -\cos(\gamma) & -R \\ \sin\left(\frac{\pi}{2} + \gamma\right) & -\cos\left(\frac{\pi}{2} + \gamma\right) & -R \\ \sin(\pi + \gamma) & -\cos(\pi + \gamma) & -R \\ \sin\left(\frac{3\pi}{2} + \gamma\right) & -\cos\left(\frac{3\pi}{2} + \gamma\right) & -R \end{bmatrix} \begin{bmatrix} v_{b,x}\\ v_{b,y}\\ \omega_{b,z} \end{bmatrix} \end{aligned} $$

Where:

• $r = 0.0297\text{m}$
• $R = 0.1325\text{m}$
• $\gamma = 0$

Simplified implementation (motor_controller.ino):

v_{Front} = -(v_y + R * omega)
v_{Left} = (v_x - R * omega)
v_{Back} = (v_y - R * omega)
v_{Right} = -(v_x + R * omega)

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Forward Kinematics

$$ \begin{aligned} \begin{bmatrix} v_{b,x}\\ v_{b,y}\\ \omega_{b,z} \end{bmatrix} &= \begin{bmatrix} 0 & 0.5 & 0 & -0.5 \\ -0.5 & 0 & 0.5 & 0 \\ -\frac{1}{4R} & -\frac{1}{4R} & -\frac{1}{4R} & -\frac{1}{4R} \end{bmatrix} \begin{bmatrix} \Delta s_1\\ \Delta s_2\\ \Delta s_3\\ \Delta s_4 \end{bmatrix} \end{aligned} $$

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Software Implementation

Motor Control (Arduino)

The motor_controller.ino uses the MobaTools library for smooth, ramped stepper control.

• Serial Parsing: Reads $v_x$, $v_y$, $\omega$ at 40Hz
• Speed Clamping: Ensures steps/sec never exceed STEPS_PER_SEC_MAX (2000 steps/s)
• Odometry Integration: Calculates and broadcasts $x$, $y$, yaw over serial

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Navigation Bridge (Python/ROS2)

The main.py node handles the Jetson-to-Arduino communication:

• Command Forwarding: Converts ROS Twist messages into serial strings
• Odometry Publishing: Publishes nav_msgs/Odometry with appropriate covariances

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Autonomous Navigation (Nav2)

Fully integrated with Nav2.

nav2_params.yaml limits:

max_vel_x: 0.25 m/s
max_vel_theta: 1.5 rad/s

This ensures reliable stepper performance without missing steps during complex maneuvers.

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License

MIT License