Model Predictive Control for Real-Time Robot Navigation
A path planner tells a robot where it should go. A controller determines how the robot should move to follow that path.
Model Predictive Control (MPC) repeatedly predicts future behavior and chooses control inputs that optimize a short horizon.
MPC Concept
Current State
|
v
Predict future states
|
v
Optimize control sequence
|
v
Apply first control
|
v
Measure new state
|
+----> Repeat
The key idea is that the entire control sequence is not executed at once. Only the first action is applied before the problem is solved again.
Robot Model
For a simple differential-drive robot:
x_dot = v cos(theta)
y_dot = v sin(theta)
theta_dot = omega
The controller can predict where the robot will be after applying candidate velocity commands.
Optimization Objective
A typical objective might penalize:
- Distance from reference path
- Heading error
- Excessive control effort
- Rapid control changes
- Collision proximity
Conceptually:
Cost =
tracking_error
+ control_effort
+ smoothness_penalty
+ obstacle_penalty
Prediction Horizon
Suppose the controller predicts:
t0 -> t1 -> t2 -> t3 -> t4
For each candidate control sequence it estimates the resulting trajectory.
The optimizer selects the best feasible sequence.
Obstacle Handling
A cost function can strongly penalize trajectories near obstacles:
Obstacle
###
#####
###
\ predicted trajectories
\---- safe
\--- unsafe
Hard constraints can also be used when collision avoidance must be guaranteed by the optimization formulation.
ROS 2 Architecture
/global_plan
|
v
/mpc
^
|
/odom /imu /local_costmap
|
v
/cmd_vel
Real-Time Requirements
MPC is computationally heavier than simple feedback controllers.
Monitor:
- Optimization time
- Control frequency
- Solver failures
- CPU utilization
- Prediction horizon
- Sensor latency
If optimization misses its deadline, the system needs a safe fallback.
Practical Implementation Strategy
Start simple:
- Define a robot model.
- Implement trajectory prediction.
- Define tracking cost.
- Add velocity constraints.
- Add acceleration constraints.
- Add obstacle constraints.
- Benchmark the solver.
- Add fallback behavior.
Why MPC Works Well for Navigation
MPC can naturally reason about:
- Future robot motion
- Vehicle dynamics
- Smooth trajectories
- Input constraints
- Obstacles
That makes it particularly attractive for robots where simple point-to-point control is insufficient.
Useful Links
- Website: https://www.v-modal.com
- SDK Flutter: https://github.com/v-modal/vmodal_sdk_flutter
- SDK Android: https://github.com/v-modal/vmodal_sdk_android
- Discord: https://discord.gg/K72z28KU
