Getting started with acados

juandavid212 · August 17, 2020, 1:54pm

Hi,
Thanks for developing such a great tool.
I’m trying to control the position of the pendulum on a cart system maintaining “-pi/2<theta<pi/2”. I’m trying to do a similar implementation to “https://www.sciencedirect.com/science/article/pii/S2405896318327204”. As the paper comments, the approach consists of setting the cost function in terms of only the control signal and imposing a terminal condition to reach the desired state.
In this sense, I should solve the NLP with:
-nlp_solver = ‘sqp’;
-nlp_solver_exact_hessian = ‘true’;
-regularize_method = ‘convexify’;
-qp_solver = ‘partial_condensing_hpipm’;
-and imposing the terminal constraint as a quadratic constraint.
How can I implement this quadratic constraint in acados?
Is there any example that I can follow?
If the cost function is only in terms of the control signal, the weight matrix in Mayer term should be W_e=zeros(nx,nx)?
Is there any disadvantage of only using the square of the control signal as a cost function in terms of the Hessian Matrix computation and convergence of the algorithm(eg. it may not get any solution or will have a slow convergence)?

Thanks in advance for your help.

FreyJo · August 20, 2020, 11:48am

Nonlinear constraints in Matlab can be formulated like here:

github.com

acados/acados/blob/master/examples/acados_matlab_octave/pendulum_dae/example_closed_loop.m#L139


      
          
          constraint_h = 1;
          if constraint_h
              nh = length(model.expr_h);
              ocp_model.set('constr_expr_h', model.expr_h);
              lh =    0;
              uh =  200;
              ocp_model.set('constr_lh', lh);
          	ocp_model.set('constr_uh', uh);
          else
              nh = 0;
          end
          
          % symbolics
          ocp_model.set('sym_x', model.sym_x);
          if isfield(model, 'sym_u')
          	ocp_model.set('sym_u', model.sym_u);
          end
          if isfield(model, 'sym_xdot')
          	ocp_model.set('sym_xdot', model.sym_xdot);
          end

There are also convex-over-nonlinear constraints, which are not part of the Matlab interface yet.

This should work, you could also set ny_e = 0 and pass empty matrices.

Penalizing the states also, can result in better conditioning and faster convergence.
But please try yourself.

Cheers