A unicycle robot moving on the plane with linear velocity v and angular velocity w can...
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A unicycle robot moving on the plane with linear velocity v and angular velocity w can be modeled by the nonlinear system: Pr = v cos 0, Py = v sin 0, 0=w, where (pr, Py) denote the Cartesian coordinates of the wheel and its orientation. Regard this as a system with input u = = [v w]¹ ER². Y I = Figure 3: Unicycle model X a) Construct a state-space model for this system in the form of f(z, u) with state: Pr cos 0+ (py - 1) sin 0 Pr sin 0+ (py 1) cos 0 0 II I2 = 13 T and output y = [172] ER² W b) Compute a local linearization for this system around the equilibrium point z* = 0, u* = 0. c) It is given that the trajectory w(t) = v(t) = 1, pr(t) = sint, py(t) = 1-cost, 0(t) = t, Vt > 0 is a solution to the system. Show that a local linearization of the system around this trajectory results in an LTI system. A unicycle robot moving on the plane with linear velocity v and angular velocity w can be modeled by the nonlinear system: Pr = v cos 0, Py = v sin 0, 0=w, where (pr, Py) denote the Cartesian coordinates of the wheel and its orientation. Regard this as a system with input u = = [v w]¹ ER². Y I = Figure 3: Unicycle model X a) Construct a state-space model for this system in the form of f(z, u) with state: Pr cos 0+ (py - 1) sin 0 Pr sin 0+ (py 1) cos 0 0 II I2 = 13 T and output y = [172] ER² W b) Compute a local linearization for this system around the equilibrium point z* = 0, u* = 0. c) It is given that the trajectory w(t) = v(t) = 1, pr(t) = sint, py(t) = 1-cost, 0(t) = t, Vt > 0 is a solution to the system. Show that a local linearization of the system around this trajectory results in an LTI system.
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Related Book For
Systems analysis and design
ISBN: 978-0136089162
8th Edition
Authors: kenneth e. kendall, julie e. kendall
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