**Note: Segway Robot project was done during the years 2011 – 2013 when Madiosn was a Master’s student. **

Study on two-wheeled robots started in late 1990 in different robotic labs in different countries.

The main objective is to design a balanced two-wheeled robot that has human-like abilities.

The main research challenge in these robots is the inherent instability of their dynamical system.

These robots can be used as autonomous vehicles in companies, factories, or just to transport people.

**Mechanical Design of Segway Robot**

**Actuator Modeling**

According to Kirchhoff law:

\[V_a – Ri – L\frac{di}{dt} – V_e = 0\]

Newton’s Law for shaft of the motor:

\[\sum M = {\tau}_m – k_f \omega – {\tau}_a = I_R \frac{d\omega}{dt}\]

Thus:

\[\begin{bmatrix} \dot{\theta}\\ \dot{\omega} \end{bmatrix} = \begin{bmatrix} 0 & 1\\ 0 & \frac{-k_m k_e}{I_R R} \end{bmatrix} \begin{bmatrix} \theta\\ \omega \end{bmatrix} + \begin{bmatrix} 0 & 0 \\ \frac{k_m}{I_R R} & \frac{-1}{I_R} \end{bmatrix} \begin{bmatrix} V_a\\ {\tau}_a \end{bmatrix}\]

\[y = \begin{bmatrix} 1 & 0 \end{bmatrix}\begin{bmatrix} \theta\\ \omega \end{bmatrix} + \begin{bmatrix} 0 & 0 \end{bmatrix}\begin{bmatrix} V_a\\ {\tau}_a \end{bmatrix}\]

**Wheel Modeling**

Applying Newton’s law in x direction and around wheel axis:

\[\sum F_x = Ma\]

\[M_w \ddot{x} = H_{fR} – H_R\]

\[\sum M_a = I \alpha\]

\[I_w \ddot{\theta} = C_R – H_{fR}r\]

**Chassis Modeling**

Applying Newton’s laws to the chassis’s free diagram:

\[I_p \ddot{\theta}_p – \frac{2k_mk_e}{Rr} \dot{x} + 2\frac{k_m}{R}V_a + M_p g \ell sin({\theta}_p) + M_p {\ell}^2 {\ddot{\theta}}_p = -M_p \ddot{x} \ell cos({\theta}_p)\]

\[2(M_w + \frac{I_w}{r^2})\ddot{x} = \frac{-2 k_m k_e}{R r^2} \dot{x} + \frac{2k_m}{R r} V_a – M_p \ddot{x} – M_p \ell {\ddot{\theta}}_p cos({\theta}_p) + M_p \ell \ddot{{\theta}_p}^2 sin({\theta}_p)\]

Linearizing the above nonlinear equations, the state equations of the system are as follows:

\[\begin{bmatrix} \dot{x}\\ \ddot{x}\\ \dot{\phi}\\ \ddot{\phi} \end{bmatrix} = \begin{bmatrix} 0 & 1 & 0 & 0\\ 0 & \frac{2 k_m k_e (M_p \ell r – I_p – M_p {\ell}^2)}{R r^2 \alpha} & \frac{{M_p}^2 g {\ell}^2}{\alpha} & 0\\ 0 & 0 & 0 & 1\\ 0 & \frac{2 k_m k_e (r \beta – M_p \ell)}{R r^2 \alpha} & \frac{M_p g \ell \beta}{\alpha} & 0 \end{bmatrix}\begin{bmatrix} x\\ \dot{x}\\ \phi\\ \dot{\phi} \end{bmatrix} + \begin{bmatrix} 0\\ \frac{2 k_m (-M_p \ell r + I_p + M_p {\ell}^2)}{R r \alpha}\\ 0\\ \frac{2 k_m (M_p \ell – r \beta)}{R r \alpha} \end{bmatrix} V_a\]

**Segway Robot Electronics**

**Motor specifications**

EMG30, DC motor with gearbox and encoder, 170 rpm speed, 1.5 kg/cm torque. Motor driver is L298 IC.

**Sensor Specifications**

GP2D12 distance measuring sensor, 10-80 cm range, 5(v) power supply, voltage output

**Designed Segway Robot Circuit in Proteus**

**Built Segway Robot **

**You can see the other posts on Mechatronics and Robotics in the link below:**

https://www.mecharithm.com/category/mechatronics/

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