Blog Post

Segway Robot (Two-Wheeled Robot)

Segway Robot (Two-Wheeled Robot)

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

segway robot design
segway robot design

Actuator Modeling

Segway Robot

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

segway robot wheels

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

segway robot chassis

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.

Segway robot motor

Sensor Specifications

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

segway robot sensor

Designed Segway Robot Circuit in Proteus

segway robot circuit

Built Segway Robot

segway robot
segway robot

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

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


If you enjoyed this post, please consider contributing to help us with the website’s running costs and keep making awesome content for you. We deeply thank you for your generous contribution!




Do not forget to contact us:

Be sure to let us know your thoughts and questions about this post as well as the other posts on the website. You can either contact us through the “Contact” tab on the website or email us at support[at]mecharithm.com.

Follow Mecharithm in the following social media too:

YouTube, and Instagram

By Madi

Ph.D. in ME | Robotics Instructor and Researcher | Founder of Mecharithm

Related Posts