If one is interested in implementing a path planning algorithm that is grid-based, one needs to consider the fact that your grid points will never represent the true state of the robot.
How is this dealt with?
Suppose we're doing path planning using a grid-based search on the side of the control for a desired grid position as an output state.
How would you handle the discrepancy between your actual starting position and your discretized starting position?
I understand that normally you may use an MPC instead, which continually recalculates an optimal path using some type of nonlinear solver, but suppose we don't do this - suppose we restrict ourselves to only a grid search and suppose at after every action the state of the robot has to be considered as living in a particular grid point.
