Advanced Control of Wheeled Inverted Pendulum Systems by Zhijun Li

By Zhijun Li

Advanced keep an eye on of Wheeled Inverted Pendulum Systems is an orderly presentation of contemporary principles for overcoming the problems inherent within the regulate of wheeled inverted pendulum (WIP) structures, 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, complicated keep watch over layout concepts and trajectory new release for WIPs. a big hindrance is tips to care for quite a few uncertainties linked to the nominal version, WIPs being characterised by means of volatile stability and unmodelled dynamics and being topic to time-varying exterior disturbances for which exact versions are difficult to return by.

The booklet is self-contained, providing the reader with every little thing from mathematical preliminaries and the fundamental Lagrange-Euler-based derivation of dynamics equations to numerous complicated movement keep watch over and strength keep an eye on methods in addition to trajectory new release approach. even if essentially meant for researchers in robot keep an eye on, Advanced keep an eye on of Wheeled Inverted Pendulum structures will even be precious examining for graduate scholars learning nonlinear platforms extra generally.

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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.

95) becomes the directional derivative of λ(x) along f (x). 96) is also a scalar field. If each component of a vector field h(x) ∈ Rm is considered to take a Lie derivative along f (x) ∈ Rn , then all components can be acted on concurrently and the result is a vector field that has the same dimension as h(x); its ith element is the Lie derivative of the ith component of h(x). Namely, if h(x) = [h1 (x), . . , hm (x)]T and each component hi (x), i = 1, . . , m is a scalar field, then the Lie derivative of the vector field h(x) is defined as ⎤ ⎡ Lf h1 (x) ⎥ ⎢ ..

12 A continuous function β : [0, a) × R+ → R+ is said to belong to class KL if, for each fixed s, the mapping β(r, s) belongs to class K with respect to r and, for each fixed r, the mapping β(r, s) is decreasing with respect to s and β(r, s) → 0 as s → ∞. It is said to belong to class KL∞ if, in addition, for each fixed s the mapping β(r, s) belongs to class K∞ with respect to r. 47) is satisfied for any initial state x(t0 ). 48) is satisfied for any initial state x(t0 ). 50) holds for an arbitrarily large a.

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