Please write/type clearly and provide explanations! Thanks.

1 Extended Kalman Filter - Linearization The motion model for a differential drive considered in the example discussed in section 6.7.3 in the lecture notes is simplified, i.e., it assumes that the robot either translates but does not rotate (v(t)?0 and r(t) 0) or it rotates but does not translate (v(t) 0 and r(t)?0). The following model instead considered the case where the robot can move along a circular arc (we assume ?t-1 for simplicity) x(t + 1)-z(t) + ye+ 1) y(t) sin ?(t) + cos ?(t) } sin(?(t) + r(t))] cos(?(t) r(t)) 1. Write the linearized motion model for this state transition equation 2. The given model is not defined when r(t.e., when the robot translates only. Write the model that should be used when the robot translates only, and write its linearization 3. Is the above model accurate for the case where the robot rotates but does not translate? Explain and your answer. If it is not, write an updated model and its linearization. 1 Extended Kalman Filter - Linearization The motion model for a differential drive considered in the example discussed in section 6.7.3 in the lecture notes is simplified, i.e., it assumes that the robot either translates but does not rotate (v(t)?0 and r(t) 0) or it rotates but does not translate (v(t) 0 and r(t)?0). The following model instead considered the case where the robot can move along a circular arc (we assume ?t-1 for simplicity) x(t + 1)-z(t) + ye+ 1) y(t) sin ?(t) + cos ?(t) } sin(?(t) + r(t))] cos(?(t) r(t)) 1. Write the linearized motion model for this state transition equation 2. The given model is not defined when r(t.e., when the robot translates only. Write the model that should be used when the robot translates only, and write its linearization 3. Is the above model accurate for the case where the robot rotates but does not translate? Explain and your answer. If it is not, write an updated model and its linearization