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Algorithmic Design of Block Backstepping Motion and Stabilization Control for Segway Mobile Robot

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Mobile Robot: Motion Control and Path Planning

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1090))

Abstract

This chapter presents a novel control algorithm based on block backstepping control approach for trajectory tracking and balancing of Segway Mobile Robot system. Two versions of block backstepping control design have been presented. The first control algorithmic design is established for nonlinear model of SMR, while the other design is devoted for linearized model. The control design objective of under-actuated SMR is to keep the inverted pendulum at the up-right position and to make the cart follow desired trajectory. Stability analysis based on zero dynamic criteria and Lyapunov theorem has been conducted such that global asymptotic stability (GAS) for the controlled SMR can be ensured. Moreover, a modification in block backstepping control design for nonlinear model has been added by introducing the integral action in the developed control laws. According to this Integral-based block backstepping control, the robustness and dynamic performance of controlled SMR has been investigated via numerical simulation. Based on numerical simulation, the results that the proposed block backstepping controllers could successfully stabilize both linearized and nonlinear underactuated systems for both regulation and tracking problems. However, the design of linear backstepping controller could keep controlled system stable with maximum initial condition of 0.523 rad, while the nonlinear control design could keep controlled system stable with maximum initial condition of 1.22 rad. Furthermore, the effect of integral action could improve both tracking performance and robust characteristics. The nonlinear block backstepping controller showed better performance in terms of dynamic behavior and error accuracy than the linear version for both regulation and tracking scenarios.

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Abbreviations

\({c}_{i} \) :

The i-th design constant with positive real values.

\({d}_{e} \) :

The error in the distance between the desired and actual values—\(m\),

D:

The separated distance between the wheels’ contact patches—\( m\)

\(e \) :

The error between desired and actual signals.

\({E}_{i} \) :

The actuating control signal for SMR system—\(V\).

\(F \) :

The applied force to the cart—\(N\)

\(g\) :

The acceleration of gravity—\(m/{s}^{2}\)

\(h\) :

The distance between wheel center and the pendulum’s center of gravity and—\(m\),

\({I}_{p}\) :

The chassis’s inertia—\(kg\cdot{m}^{2}\)

\({I}_{pdel}\) :

Inertia due to rotation of chassis—\(kg\cdot{m}^{2}\)

\({\mathrm{I}}_{\mathrm{w}}\) :

The wheel Inertia \(-kg\cdot{m}^{2}\)

\(K\) :

Kinetic energy—\(Joule\),

\({k}_{e}\) :

The constant of Back emf,

\({k}_{f}\) :

The frictional constant,

\({k}_{i}\) :

The controller’s design parameters,

\({k}_{m}\) :

The motor’s constant—\(N\cdot{m}/{A}\),

\({M}_{p}\) :

The chassis’s mass—\(kg\),

\({M}_{w}\) :

The wheel’s mass—\(kg\),

\(R \) :

The resistance of armature coil of DC motor—\(\Omega \),

\(r \) :

The radius of cart’s wheel—\(m\),

\(T\) :

The generated torque due to actuating motors—\(N\cdot{m}\),

\({V}_{p}\) :

The potential energy—\(Joule\),

\(V\left(.\right)\) :

The Lyapunov function (L.F.),

\({X}_{c}\) :

The linear displacement of SMR—\(m\),

\({z}_{1} \) :

The regulated variable in the block backstepping control design,

\(\alpha \) :

The stabilization function,

\({\delta }_{d}\) :

The error of heading angle,

\({\lambda }_{i}\) :

The design constant of arbitrary positive-real value,

\(\varphi \) :

The angle of SMR rotation—\(rad\),

\(\theta \) :

The angular position of pendulum w.r.t vertical axis—\( rad\).

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Acknowledgements

The authors would like to thank Prince Sultan University, Riyadh, Saudi Arabia for supporting this work. Special acknowledgement to Automated Systems & Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Control and Systems Engineering Department, University of Technology-Iraq, Baghdad, Iraq

    Amjad J. Humaidi

  2. State Company for Oil Projects-Ministry of Oil-Iraq, Baghdad, Iraq

    Mustafa R. Hameed

  3. Technical Engineering College, Middle Technical University, Baghdad, Iraq

    Alaq F. Hasan

  4. Taylor’s University, Taylor’s Lakeside Campus, Subang Jaya, Selangor, Malaysia

    Abdulkareem Sh. Mahdi Al-Obaidi

  5. College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia

    Ahmad Taher Azar

  6. Automated Systems and Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia

    Ahmad Taher Azar

  7. Faculty of Computers and Artificial Intelligence, Benha University, Benha, Egypt

    Ahmad Taher Azar

  8. Department of Computer Techniques Engineering, Dijlah University College, Baghdad, 10022, Iraq

    Ibraheem Kasim Ibraheem

  9. Electrical Engineering Technical College, Middle Technical University, Baghdad, Iraq

    Ayad Q. Al-Dujaili

  10. Department of Computer Science, Edge Hill University, Ormskirk, UK

    Ammar K. Al Mhdawi

  11. Aeronautical Department, College of Technical Engineering, Alfarahidi University, Baghdad, 10070, Iraq

    Farah Ayad Abdulmajeed

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  1. Amjad J. Humaidi
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  6. Ibraheem Kasim Ibraheem
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Correspondence to Amjad J. Humaidi .

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Editors and Affiliations

  1. Faculty of Computers and Artificial Intelligence, Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Electrical Engineering Department, University of Baghdad, College of Engineering, Baghdad, Iraq

    Ibraheem Kasim Ibraheem

  3. University of Technology, Baghdad, Iraq

    Amjad Jaleel Humaidi

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Humaidi, A.J. et al. (2023). Algorithmic Design of Block Backstepping Motion and Stabilization Control for Segway Mobile Robot. In: Azar, A.T., Kasim Ibraheem, I., Jaleel Humaidi, A. (eds) Mobile Robot: Motion Control and Path Planning. Studies in Computational Intelligence, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-031-26564-8_16

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