Control Design and Analysis for Underactuated Robotic by Xin Xin, Yannian Liu

By Xin Xin, Yannian Liu

The final twenty years have witnessed enormous growth within the research of underactuated robot platforms (URSs). Control layout and research for Underactuated Robotic Systems offers a unified remedy of keep an eye on layout and research for a category of URSs, which come with platforms with multiple-degree-of-freedom and/or with underactuation measure . It offers novel notions, beneficial properties, layout thoughts and strictly worldwide movement research effects for those platforms. those new fabrics are proven to be very important in learning the regulate layout and balance research of URSs.

Control layout and research for Underactuated robot Systems contains the modelling, keep watch over layout and research awarded in a scientific method quite for the next examples:

l at once and remotely pushed Acrobots

l Pendubot

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 loose flying robot

The theoretical advancements are established by way of experimental effects for the remotely pushed Acrobot and the rotational pendulum.

Control layout and research for Underactuated Robotic Systems is meant for complex undergraduate and graduate scholars and researchers within the region of keep an eye on structures, mechanical and robotics platforms, nonlinear structures and oscillation. this article is going to not just permit the reader to achieve a greater realizing of the facility and primary boundaries of linear and nonlinear keep watch over conception for the keep watch over layout and research for those URSs, but additionally encourage the reader to handle the demanding situations of extra complicated URSs.

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0 0 .. ··· 0 −1 1 0 0 .. 30) where δw, δq, and δθ are small variations of the work, q, and θ , respectively. 31) which holds for all δq. Therefore, we obtain T τ = R u, u= R T −1 τ. 32) 30 2 Fundamental Background Below, we derive the motion equation for the robot using the Euler–Lagrange equation in terms of the coordinate θ with input u, and then transform to the coordinate q with input τ . To this end, we need to obtain the kinetic and potential energy of the robot. 33) ⎪ ⎩ 0, j > i.

28]. Moreover, we present some known properties and one new property of the robot. We assume that the robot is free of friction and other disturbances. 1 Motion Equations Consider the robot in Fig. 2. Let qi (i = 1, 2, . . , n) be the relative angle between links i − 1 and i, that is, the angle measured counter-clockwise from the extension line of link i − 1 to link i, and link 0 is defined to be the positive Y -axis. For the ith link, mi is its mass, li is its length, lci is the distance from joint i to the COM of the ith link, and Ji is the moment of inertia around its COM.

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. 72). Fourth, we introduce a property 2 ≤ mi li lci , Ji + mi lci i = 1, 2, . . 74) which is important in the motion analysis of several underactuated robotic systems in this book. To show this, let z be the distance from a point in the link i to the joint i.

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