Model Predictive Control for Real-Time Robot Navigation

Model Predictive Control (MPC) enables real-time robot navigation by repeatedly predicting future states and optimizing control inputs. The process involves:

1. Estimating future behavior

2. Choosing control inputs that optimize performance over a short horizon

3. Applying the first control input

4. Measuring the new state

5. Repeating the process

The controller only applies the first control input before solving the problem again. For a simple differential-drive robot, the model predicts future positions using:

x_dot = v cos(theta)

y_dot = v sin(theta)

theta_dot = omega

The optimization objective typically penalizes:

- Distance from reference path

- Heading error

- Excessive control effort

- Rapid control changes

- Proximity to collisions

The prediction horizon determines how far into the future the controller predicts states. Hard constraints can guarantee collision avoidance by incorporating them into the optimization formulation.

MPC is computationally heavier than simple feedback controllers but works well for navigation due to its ability to reason about future motion, vehicle dynamics, smooth trajectories, input constraints, and obstacles. Practical implementation starts with defining a robot model, implementing trajectory prediction, setting tracking cost, adding velocity and acceleration constraints, and finally adding obstacle constraints. If optimization misses its deadline, a safe fallback behavior is required.