MPC Quadcopter

Model Predictive Control for an autonomous quadcopter (UAV)

• System modelling
  • State-Space model
  • Linearization
• Controller design
  • PID SISO control approach
  • MPC MIMO control approach
  • Observers: Kalman filter
• Simulation
  • PID simulation
  • MPC simulation (linear model)
  • Real-Time simulation (non-linear model)

(Under construction)

Model predictive control (MPC)

Quadcopter simulation

Algorithm

• Initialization of the variables

• Get the augmented incremental model and the parameters of the control trajectories vector (DeltaU) based on the state-space system, the control horizon (Nc) and prediction horizon (Np)

  • Augmented incremental model

    

    

    

  • Incremental control trajectory vector (DeltaU) obtained from the cost function minimization

    

    

    

    

• Calculate the constant part of DeltaU

• Control loop

  • Read input signal

  • Calculate the variable part of DeltaU

  • Add both parts and apply the receding horizon control extracting first element

  • Get the control signal

    

  • Get the incremental system state

    

Figures from [1]

MPC with output constraints

• In the initialization variables:

  • Create M matrix

• In the control loop:

  • Calculate the gamma matrix with the constraints of the output
  • Recalculate DeltaU from optimization with restrictions

  Constraint output / u / delta u:

  

Figures from [1]

References

[1] Sistemas de control en tiempo real para aplicaciones industriales: Teoría, problemas y prácticas - Ramón Guzmán 2020

[2] Dynamic Modeling and Control of a Quadrotor Using Linear and Nonlinear Approaches - H. M. Nabil ElKholy - 2014

[3] Decentralized Navigation of Multiple Quad-rotors using Model Predictive Control - I. Khan - 2017