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Model Predictive Control for Real-Time Robot Navigation

#robotics #mpc #controlsystems #ros2

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
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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
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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
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Prediction Horizon

Suppose the controller predicts:

t0 -> t1 -> t2 -> t3 -> t4
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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
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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
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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:

  1. Define a robot model.
  2. Implement trajectory prediction.
  3. Define tracking cost.
  4. Add velocity constraints.
  5. Add acceleration constraints.
  6. Add obstacle constraints.
  7. Benchmark the solver.
  8. 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

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