question archive On a 2D plane, the robot has an x coordinate, a y coordinate, and a theta orientation
On a 2D plane, the robot has an x coordinate, a y coordinate, and a theta orientation
Subject:PhysicsPrice: Bought3
On a 2D plane, the robot has an x coordinate, a y coordinate, and
a theta orientation. It moves with linear velocity v, and angular velocity omega.
The state vector s_t for this robot is: s_t = [x y theta]'
The input control u_t for the robot is: u_t = [v omega]'
The robot can make an observation z_t of a landmark using a LIDAR sensor. The sensor reports the range of the landmark rho and the bearing to the landmark phi: z_t = [rho phi]'
You will need some trig for this assignment, so if you need to brush up on your sines and cosines.
Question 1
Write down the range of the robot rho in terms of the landmark's coordinates (m_x, m_y), and the robot's coordiantes (x,y).
Question 2
Write down the bearing of the robot phi in terms of the landmark's coordinates (m_x, m_y), and the robot's coordiantes (x,y).
Hint: You'll want to use atan2().
Question 3
With the answers to 1 and 2, write down the function h(s_t).
Question 4
The robot can be thought of moving along circumference of a circle with radius
r = v/omega The velocity vector of the robot can be broken down into x and y components. What are vx and vy, given theta?
Let's say that v and omega remain constant over a small time period dt. If the robot starts at x and y with orientation theta, and it's traveling at v and omega, where will the robot be after dt?
Question 5
-x update
-y update
-theta updateQuestion 6
With the answers to 5, write down the function g(s_t,u_t).
