By Xin Xin, Yannian Liu
The final twenty years have witnessed substantial growth within the examine of underactuated robot platforms (URSs). Control layout and research for Underactuated Robotic Systems offers a unified remedy of regulate layout and research for a category of URSs, which come with structures with multiple-degree-of-freedom and/or with underactuation measure . It offers novel notions, positive factors, layout innovations and strictly worldwide movement research effects for those structures. those new fabrics are proven to be very important in learning the keep an eye on layout and balance research of URSs.
Control layout and research for Underactuated robot Systems comprises the modelling, keep watch over layout and research offered in a scientific approach rather for the subsequent examples:
l without delay and remotely pushed Acrobots
l rotational pendulum
l counter-weighted Acrobot
2-link underactuated robotic with versatile elbow joint
l variable-length pendulum
l 3-link gymnastic robotic with passive first joint
l n-link planar robotic with passive first joint
l n-link planar robotic with passive unmarried joint
double, or parallel pendulums on a cart
l 3-link planar robots with underactuation measure two
2-link unfastened flying robot
The theoretical advancements are demonstrated by means of experimental effects for the remotely pushed Acrobot and the rotational pendulum.
Control layout and research for Underactuated Robotic Systems is meant for complicated undergraduate and graduate scholars and researchers within the quarter of keep an eye on platforms, mechanical and robotics platforms, nonlinear structures and oscillation. this article will not just permit the reader to achieve a greater realizing of the facility and primary obstacles of linear and nonlinear regulate idea for the keep watch over layout and research for those URSs, but additionally encourage the reader to deal with the demanding situations of extra advanced URSs.
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Extra info for Control Design and Analysis for Underactuated Robotic Systems
Second, we show a property for the n-link planar robot shown in Fig. 65) ˙ M(q) − 2C(q, q) ˙ is a skew-symmetric matrix. , in . The above property is useful in control design and analysis of robotic systems . 68) which shows that is a skew-symmetric matrix. 65). 66). 70) where P (q) is defined by n P (q) = i βi cos qj . 71) j =1 i=1 A property of the robot is T T E˙ = τ q˙ = u θ˙ . 66). An alternative and direct way is to use the following relation of small variation of the total mechanical energy and the work: δE = δw.
1 Lyapunov Stability Theory Stability theory plays an important role in systems theory and engineering. There are many different kinds of stability issues in studying dynamical systems. For the purpose of this book, in this chapter, we will introduce the knowledge needed in this book about stability of equilibrium points for autonomous systems. We focus on Lyapunov stability theory, and the contents of this section are mainly taken from [30, 39, 78]. 2) for some constant L and all x0 ∈ D0 . The function f (x) is said to be Lipschitz on the set D if it satisfies the local Lipschitz condition uniformly (with the same constant L) at all points x0 ∈ D.
133), at which the control input torque becomes infinity. 132) holds are proposed. 8) is bounded from below, then there exist positive parameters kD such that Λ is globally positive definite. 8) is bounded from below for all the underactuated robotic systems in this book except the variable length pendulum (VLP) studied in Chap. 8. 132) holds for all the underactuated robotic systems except the VLP studied in Chap. 8. Since the total mechanical energy of the VLP is not bounded from below, we study the partial energy shaping instead.
Control Design and Analysis for Underactuated Robotic Systems by Xin Xin, Yannian Liu