Velocity and position control of a wheeled inverted pendulum by partial feedback linearization

In this paper, the dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while tak...

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Bibliographic Details
Published in:IEEE transactions on robotics 2005-06, Vol.21 (3), p.505-513
Main Authors: Pathak, K., Franch, J., Agrawal, S.K.
Format: Article
Language:English
Subjects:
Applied sciences
Comparative analysis
Computer science
control theory
systems
Control system synthesis
Control systems
Control theory. Systems
Controllability
Dynamical systems
Equations
Exact sciences and technology
Feedback
Lyapunov methods
Mobile robots
modeling
Nonlinear systems
Position control
Vehicle dynamics
Vehicles
Velocity
Velocity control
Wheels
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Summary:In this paper, the dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations. This model is compared with the previous models derived for similar systems. The strong accessibility condition is checked and the maximum relative degree of the system is found. Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated. The resulting equations are then used to design two novel controllers. The first one is a two-level velocity controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch (pendulum angle from the vertical) within a specified range. The second controller is also a two-level controller which stabilizes the vehicle's position to the desired point, while again keeping the pitch bounded between specified limits. Simulation results are provided to show the efficacy of the controllers using realistic data.
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2004.840905