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The robot in the image is sending out a green dashed line toward a cylindrical object, representing a measurement (probably range + bearing). This is typical of range-bearing sensing, where you get both:- Distance (range) to the object- Direction (bearing) of the object However, uncertainty in these sensors makes localization of objects ambiguous. Banana Shape Problem - A common nonlinear unce..

If I know exactly where the vehicle will be next, there is no uncertainty. For example, If \( d_R = 1\,\mathrm{m}, \quad d_L = 0.8\,\mathrm{m} \), meaning- The right wheel travels 1 meter.- The left wheel travels 0.8 meters.- Since these distances are not equal, the robot will turn (instead of moving straight).- \( d \propto C \quad \text{or} \quad d = \alpha C \) meaning the distance moved (d)..

Each pose (at time step i) is represented as:\[ \mathbf{X}_i = [x, y, z, r, p, h]^\top \]This is the 6-DoF (degrees of freedom) pose of the robot at one point in time.If the robot moves through multiple time steps: \[ X = \begin{bmatrix} X_1 \\ X_2 \\ \vdots \\ X_n \end{bmatrix} \]This concatenates all poses into one large state vector over a trajectory or sequence of observations.- Since full s..

Root Shifting - Which is about changing the reference coordinate frame (or "root") used to describe 3D positions and orientations.- You have data (like a 3D map or trajectory) that’s expressed in the global frame {g}, but now you want to express that data in a local or vehicle frame {v} instead.- Because sometimes it’s easier or more useful to:View motion relative to the robotAlign local mapsDo..

6-DOF (Degrees of Freedom) - In 3D space, any rigid body (like a robot or camera) has 6 degrees of freedom: 3 for position → translation in x,y,zx, y, zx,y,z3 for orientation → rotation in roll, pitch, and yawSo the pose is written as a vector:\[ \mathbf{X} = [x, y, z, r, p, h] \] x,y,z: translation in metersr = roll (rotation around x-axis)p = pitch (rotation around y-axis)h = heading or yaw (r..