Advanced Control of Wheeled Inverted Pendulum Systems by Zhijun Li

By Zhijun Li

Advanced regulate of Wheeled Inverted Pendulum Systems is an orderly presentation of contemporary rules for overcoming the problems inherent within the keep an eye on of wheeled inverted pendulum (WIP) platforms, within the presence of doubtful dynamics, nonholonomic kinematic constraints in addition to underactuated configurations. The textual content leads the reader in a theoretical exploration of difficulties in kinematics, dynamics modeling, complex keep watch over layout thoughts and trajectory iteration for WIPs. an immense situation is the best way to take care of a variety of uncertainties linked to the nominal version, WIPs being characterised via volatile stability and unmodelled dynamics and being topic to time-varying exterior disturbances for which exact types are tough to come back by.

The ebook is self-contained, delivering the reader with every little thing from mathematical preliminaries and the fundamental Lagrange-Euler-based derivation of dynamics equations to varied complex movement regulate and strength keep watch over methods in addition to trajectory iteration approach. even though essentially meant for researchers in robot regulate, Advanced regulate of Wheeled Inverted Pendulum structures will even be invaluable examining for graduate scholars learning nonlinear platforms extra generally.

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44 (LaSalle’s Theorem) Let Ω be a compact invariant set Ω = x ∈ Rn : V˙ (x) = 0 and V : Rn → R be a locally positive definite function such that on the compact set we have V˙ (x) ≤ 0. , its α limit set is contained inside the largest invariant set in Ω. In particular, if Ω contains no invariant sets other than x = 0, then 0 is asymptotically stable. 111) and let the origin be an equilibrium point, V (x) : N → R be a continuously differentiable positive definite function on a neighborhood N of the origin, such that V˙ (x) ≤ 0 in N , then the origin is asymptotically stable if there is no solution that can stay forever in S = x ∈ N | V˙ (x) = 0, other than the trial solution.

60) 48 3 Modeling of WIP Systems To facilitate the understanding of the control problems, and to help design controllers for the above systems, it is essential to have a thorough study of the mathematical properties of the system. 5 Properties of Mechanical Dynamics There are some properties summarized for the dynamics of wheeled inverted pendulum, which is convenient for controller design. , M(q) = M T (q). e. ∃0 < α ≤ β < ∞, such that αIn ≤ M(q) ≤ βIn , ∀q ∈ Rn , where In is the n × n identity matrix.

Gm , adf g1 , . . , adf gm , . . , adn−1 f g1 , . . 94) With the control Lie algebra concept, we can show that the following theorem is true and is also a general effective testing criterion for system controllability. 89) is controllable if and only if dim(Δ) = dim(Ωx ) = n. Note that because each element in Δ is a function of x, the dimension of Δ may be different from one point to another. 89) is locally controllable. On the other hand, if the condition of dimension can cover all of region Ωx , then it is globally controllable.

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