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Model Predictive Control (MPC) & Model Predictive Contouring Control (MPCC)

Implemented:

  • CasADi (found in folder casadi_):
    • MPC and MPCC for kinematic car model with combination of methods Direct Multiple Shooting (DMS)/Direct Collocation (DC) and solvers MA57/MUMPS
  • acados (found in folder acados_)
    • MPC and MPCC for kinematic car model with method DMS and solver Partial Condensing HPIPM

Running demos

Two options are available for demos, either plotting a single trajectory computed by the MPC(C) or displaying an animation of the entire path from the starting location to the target location. Some configurable options for the default models (i.e. time horizon, number of control intervals, etc.) are available in mpc(c)/config.py. Demos are run via run.py.

Editing models for CasADi

By default, all solvers in solvers/ use the car kinematic model. For example, mpcc_[method].py uses the following system of equations and controls:

car_system

car_controls

Which looks like this in the code:

## System Variables
x = cd.SX.sym('x')
y = cd.SX.sym('y')
phi = cd.SX.sym('phi')
delta = cd.SX.sym('delta')
vx = cd.SX.sym('vx')
theta = cd.SX.sym('theta')

z = cd.vertcat(x, y, phi, delta, vx, theta)

## Control variables
alphaux = cd.SX.sym('alphaux')
aux = cd.SX.sym('aux')
dt = cd.SX.sym('dt')

u = cd.vertcat(alphaux, aux, dt)

zdot = cd.vertcat(vx*cd.cos(phi), vx*cd.sin(phi), (vx/inter_axle)*cd.tan(delta), alphaux, aux, vx*dt)

Therefore, using a different model requires declaring all the relevant system variables s1 = cd.SX.sym('s1'); s2 = cd.SX.sym('s2'); ..., control variables c1 = cd.SX.sym('c1'); c2 = cd.SX.sym('c2'); ... and them combining them into the system vector z = cd.vertcat(s1, s1, ...), control vector u = cd.vertcat(c1, c2, ...). Additionally, change the zdot vector according to the new system constraints. Make sure to also edit the bounds (lbw & ubw) in the NLP formulation.

Editing models for acados

Models are located in the model.py folder. They are implemented in CasADI, so use the same directions as the previous section.

Installing HSL solvers

See hsl.md for instructions if CasADI is installed via pip.