By Zhijun Li

ISBN-10: 1447129628

ISBN-13: 9781447129622

ISBN-10: 1447129636

ISBN-13: 9781447129639

*Advanced keep watch over o**f Wheeled Inverted Pendulum Systems* is an orderly presentation of modern principles for overcoming the problems inherent within the keep watch over 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 thoughts and trajectory iteration for WIPs. a huge obstacle is easy methods to take care of quite a few uncertainties linked to the nominal version, WIPs being characterised via risky stability and unmodelled dynamics and being topic to time-varying exterior disturbances for which actual types are tough to come back 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 regulate and strength keep an eye on methods in addition to trajectory new release process. even if essentially meant for researchers in robot keep an eye on, *Advanced keep an eye on of Wheeled Inverted Pendulum platforms *will even be valuable examining for graduate scholars learning nonlinear structures extra generally.

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**Additional resources for Advanced Control of Wheeled Inverted Pendulum Systems**

**Example text**

The wheel actuators rotate the wheels with respect to the chassis. The motion control unit controls the wheel actuators so as to move the vehicle and stabilize the inverted pendulum. Under such a configuration, the vehicle is characterized by the ability to balance on the two wheels and spin on the spot. , how the forces acting on robots make these robots move by their kinematics. Mathematically, the kinematic equations establish a mapping between the Cartesian space positions/orientations and the joint space positions (translation or revolution).

100) be given with f (x0 , 0) = 0 and f (x, u) continuously differentiable in a neighborhood of (x0 , 0). A necessary condition for the existence of a continuously differentiable control law that makes (x0 , 0) asymptotically stable is that 1. the linearized system should have no uncontrollable modes associated with eigenvalues whose real part is positive; 2. there exists a neighborhood Ω of (x0 , 0) such that for each ξ ∈ Ω there exists a control uξ defined on [0, ∞) such that this control steers the solution of x˙ = f (x, uξ ) from x = ξ at t = 0 to x = x0 at t = ∞; 3.

If f is bounded can also lead to f → 0 as t → ∞. However, we have the following results. 24 (Barbalat’s Lemma) Consider the function φ : R+ → R. 25 Assume that a nonnegative scalar differentiable function f (t) enjoys the following conditions 1. d f (t) ≤ k1 f (t) dt ∞ 2. f (t) dt ≤ k2 0 for all t ≥ 0, where k1 and k2 are positive constants, then limt→∞ f (t) = 0. 81) f (s) ds ≥ f (0) − k1 k2 0 These inequalities imply that f (t) is a uniform bounded function. , f (t) ≤ k3 with k3 a positive constant.

### Advanced Control of Wheeled Inverted Pendulum Systems by Zhijun Li

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