Appendix Y" YA O' Fig 1. Kinematics of the robotic vehicle The non-linear, kinematics model of the robot is described by the following equations: x(t) = v(t)cos((t)) + wx y(t) = v(t)sin(0(t)) + wy (t) = w(t) + Wo where, the state of the system is defined as X = [x,y,0], the inputs are defined as X = [v,w] and w=[Wx, Wy, We]" is white, Gaussian (process) noise with an assumed distribution given by w ~N(0,Q). The odometer data directly measures the state of the system; accordingly, the measurement equation (excluding the sonar data) is given by, [100] YCXn010X+n 10 0 1 where, n is white, Gaussian (sensor) noise with an assumed distribution given by n~ N(O, R). Define the state transition and observation models based on the kinematics of the robotic vehicle.