By Wen-Hong Zhu (auth.)

Driven via the necessity to in attaining greater keep an eye on performances for robots with hyper levels of freedom, the digital decomposition regulate method is punctiliously offered during this e-book. This strategy makes use of subsystem (such as hyperlinks and joints of a fancy robotic) dynamics to behavior regulate layout, whereas making certain the soundness and convergence of the total advanced robotic with no compromising the rigorousness of the procedure analysis.

The principal thought of this strategy is the definition of the digital balance. the soundness of the total complicated robotic is mathematically reminiscent of the digital balance of each subsystem. This truth permits us to transform a wide challenge to some basic issues of mathematical walk in the park.

This e-book contains fourteen chapters. the 1st 5 chapters shape the root of this method. the remainder 9 chapters are quite self sustaining. ranging from bankruptcy 6, every one bankruptcy bargains with a selected kind of structures together with motor/transmission assemblies, hydraulic robots, coordinated a number of robots, house robots, humanoid robots, adaptive teleoperation, and modular robotic manipulators. on the finish, the extensions of this method of distributed-parameter structures and to electric circuits are given, paving the best way for different functions to stick with.

This e-book is meant for practitioners, researchers, and graduate scholars who've obtained basic wisdom on robotics and regulate structures and feature been dedicated to reaching the easiest keep watch over performances on advanced robotics structures and past.

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**Example text**

5. 6. 7, the two projection functions to be used in parameter adaptation were given. Unlike conventional parameter adaptation that is persistently driven by control errors, the projection functions used in this book impose limits on parameter estimates to prevent them from drifting. Corresponding lemmas guarantee that parameter estimates with limits can be smoothly incorporated into respective controllers without jeopardizing the stability properties. These ﬁve sections constitute the basic contents of the virtual decomposition control (VDC) computations which extensively use body-frame referenced rigid body dynamics and kinematics-based velocity/force transformations.

2 Mathematical Preliminaries In this chapter, mathematical tools to be used throughout this book are given. Starting from notation, this chapter presents spaces and groups ﬁrst. After that, vectors and coordinate systems are introduced, particularly the body-frame referenced vector expressions are emphasized. Orientations expressed by quaternions are given. Then, linear/angular velocity vectors and force/moment vectors are deﬁned, leading to the rigid body dynamics expressed in a body frame. Two functions to be used in the parameter adaptation are subsequently deﬁned.

65) denotes a force/moment transformation matrix that transforms the force/ moment vector measured and expressed in frame {B} to the same force/moment vector measured and expressed in frame {A}. 39), and A rAB ∈ R3 denotes a vector from the origin of frame {A} to the origin of frame {B}, expressed in frame {A}. It is obvious that B UA ∈ R6×6 is constant. 60), both B V ∈ R6 and BF ∈ R6 are having exactly the same deﬁnitions by substituting frame {B} for frame {A}. 3. 64) indicate the duality between the linear/angular velocity transformations and the force/moment transformations.