– A robot’s hand is initially at a location and orientation given by Told, after execute a series of transnational and rotational motions, its new location and orientation is given by Tnew [10 0 4 | 0 0 -1 -3 Told = 1 01 0 7 Loo 0 1 [i 0 0 4.3 1 0 0 -1.2 -3.2 Tnew = 0 0.8 0 6.8 [0 0 0 1 (a) (10 points) Compute the differential operator A assuming the change is very small. (b) (5 points) There exists a transformation matrix Q that would accomplish the transforma- tion from Told to Tnew. That is Tnew = QTold. Compute this Q matrix. (c) (7 points) By inspection, what is the differential translation that constitutes this Q ma- trix. (d) (8 points) By inspection, what is the differential rotation that constitutes this Q matrix. (hint: look into the topic about the differential rotation about a general axis q) (e) (10 points) What is the mathematical relationship between A and Q (hint: start with the relation: Tnew = Told + dT) Show transcribed image text – A robot’s hand is initially at a location and orientation given by Told, after execute a series of transnational and rotational motions, its new location and orientation is given by Tnew [10 0 4 | 0 0 -1 -3 Told = 1 01 0 7 Loo 0 1 [i 0 0 4.3 1 0 0 -1.2 -3.2 Tnew = 0 0.8 0 6.8 [0 0 0 1 (a) (10 points) Compute the differential operator A assuming the change is very small. (b) (5 points) There exists a transformation matrix Q that would accomplish the transforma- tion from Told to Tnew. That is Tnew = QTold. Compute this Q matrix. (c) (7 points) By inspection, what is the differential translation that constitutes this Q ma- trix. (d) (8 points) By inspection, what is the differential rotation that constitutes this Q matrix. (hint: look into the topic about the differential rotation about a general axis q) (e) (10 points) What is the mathematical relationship between A and Q (hint: start with the relation: Tnew = Told + dT)

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Answer to – A robot’s hand is initially at a location and orientation given by Told, after execute a series of transnational and r…