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By Mark W. Spong

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We also introduce the notion of feedforward control and the techniques of computed torque and inverse dynamics as a means for compensating the complex nonlinear interaction forces among the links of the manipulator. Robust and adaptive control are introduced in Chapter 8 using the Second Method of Lyapunov. Chapter 10 provides some additional advanced techniques from nonlinear control theory that are useful for controlling high performance robots. 24 INTRODUCTION Force Control Once the manipulator has reached location A.

1-9 List five applications where either tactile sensing or force feedback control would be useful in robotics. 1-10 Find out how many industrial robots are currently in operation in the United States. How many are in operation in Japan? What country ranks third in the number of industrial robots in use? 1-11 Suppose we could close every factory today and reopen then tomorrow fully automated with robots. What would be some of the economic and social consequences of such a development? 1-12 Suppose a law were passed banning all future use of industrial robots.

3. It is an operator taking a vector and rotating it to a new vector in the same coordinate system. ROTATIONAL TRANSFORMATIONS 41 The particular interpretation of a given rotation matrix R that is being used must then be made clear by the context. 1 Similarity Transformations A coordinate frame is defined by a set of basis vectors, for example, unit vectors along the three coordinate axes. This means that a rotation matrix, as a coordinate transformation, can also be viewed as defining a change of basis from one frame to another.

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