Nonlinear Model Predictive Control (NMPC)

Problem Statement

NMPC optimizes constrained control over a finite horizon using the full nonlinear UAV model. It handles state and input constraints explicitly while tracking aggressive trajectories.

Model and Formulation

At each control step solve:

$$ \min_{u_{0:N-1}} \sum_{k=0}^{N-1}\left(|x_k-x_k^{ref}|_Q^2 + |u_k-u_k^{ref}|_R^2\right) + |x_N-x_N^{ref}|_P^2 $$

subject to:

$$ x_{k+1}=f(x_k,u_k),\quad u_{min}\le u_k \le u_{max} $$

Algorithm Procedure

1. Warm-start control sequence from previous solution.
2. Integrate dynamics (single-shooting/multiple-shooting).
3. Solve nonlinear program under constraints.
4. Apply first control action, then shift horizon.

Tuning Guidance

• Increase terminal weight P to improve horizon-end stability.
• Use shorter horizons for strict realtime budgets.
• Start with soft constraints before switching to hard constraints.

Failure Modes and Diagnostics

• Solver infeasibility appears under inconsistent references or tight bounds.
• Poor warm starts increase optimization latency.
• Inaccurate models produce biased constraint activity.

Implementation and Execution

python -m uav_sim.simulations.trajectory_tracking.nmpc

Evidence

References

• Diehl et al., Real-Time Optimization and NMPC (2002)
• Rawlings, Mayne, Diehl, Model Predictive Control: Theory, Computation, and Design

Related Algorithms

• MPPI
• LQR Hover