Linear Kinematic Model

IV . PURE PURSUIT ALGORITHM
One of the most popular classes of path tracking methods found in robotics is that of geometric path trackers. These methods exploit geometric relationships between the vehicle and the path resulting in control law solutions to the path tracking problem. These techniques often make use of a look ahead distance to measure error ahead of the vehicle.
The pure pursuit algorithm pursues a point along the path that is located at a certain distance away from the vehicle’s current position. The algorithm is relatively simple and easy to implement, and is robust to disturbances and large lateral error. Fig 4. Pure pursuit strategy
The pure pursuit method consists of geometrically calculating the curvature of a circular

Linear kinematic model is used to estimate the vehicle location. The vehicle moves at a velocity of 8 m/s. The cross track error plot and comparison of vehicle orientation error and commanded steering input to reduce the orientation error are shown in the second plot. Fig 4:Straight line path tracking using non-linear kinematic model and error plot
Fig 4 shows the straight line path tracking using a non-linear kinematic model. The second figure shows the cross track error plot and comparison of vehicle orientation error and commanded steering input to reduce the orientation error.
Fig 5 shows the tracking of a circular path . Linear kinematic model is used to estimate the vehicle location. The vehicle moves at a velocity of 5 m/s. The second figure shows the cross track error plot and comparison of vehicle orientation error and commanded steering input to reduce the orientation error. The steering angle is constrained to be within ± 450 and the steering angle rate is constrained to ± 2.50. The average cross track error was found to be 0.88311 m.

Fig 5:Circular path tracking using linear kinematic model and error plot Fig 6:Circular path tracking using non- linear kinematic model and error