Minimal example: use GN Hessian, improve warning (acados#1135)

examples/acados_python/getting_started/minimal_example_ocp.py

@@ -31,6 +31,7 @@
 from acados_template import AcadosOcp, AcadosOcpSolver
 from pendulum_model import export_pendulum_ode_model
 import numpy as np
+import casadi as ca
 from utils import plot_pendulum
 
 def main():
@@ -52,16 +53,21 @@ def main():
     # set prediction horizon
     ocp.solver_options.tf = Tf
 
-    # set cost
+    # cost matrices
     Q_mat = 2*np.diag([1e3, 1e3, 1e-2, 1e-2])
     R_mat = 2*np.diag([1e-2])
 
-    # the 'EXTERNAL' cost type can be used to define general cost terms
-    # NOTE: This leads to additional (exact) hessian contributions when using GAUSS_NEWTON hessian.
-    ocp.cost.cost_type = 'EXTERNAL'
-    ocp.cost.cost_type_e = 'EXTERNAL'
-    ocp.model.cost_expr_ext_cost = model.x.T @ Q_mat @ model.x + model.u.T @ R_mat @ model.u
-    ocp.model.cost_expr_ext_cost_e = model.x.T @ Q_mat @ model.x
+    # path cost
+    ocp.cost.cost_type = 'NONLINEAR_LS'
+    ocp.model.cost_y_expr = ca.vertcat(model.x, model.u)
+    ocp.cost.yref = np.zeros((nx+nu,))
+    ocp.cost.W = ca.diagcat(Q_mat, R_mat).full()
+
+    # terminal cost
+    ocp.cost.cost_type_e = 'NONLINEAR_LS'
+    ocp.cost.yref_e = np.zeros((nx,))
+    ocp.model.cost_y_expr_e = model.x
+    ocp.cost.W_e = Q_mat
 
     # set constraints
     Fmax = 80

interfaces/acados_template/acados_template/acados_ocp.py

@@ -201,7 +201,7 @@ def make_consistent(self) -> None:
             if opts.hessian_approx == 'GAUSS_NEWTON' and opts.ext_cost_num_hess == 0 and model.cost_expr_ext_cost_custom_hess_0 is None:
                 print("\nWARNING: Gauss-Newton Hessian approximation with EXTERNAL cost type not possible!\n"
                 "got cost_type_0: EXTERNAL, hessian_approx: 'GAUSS_NEWTON.'\n"
-                "GAUSS_NEWTON hessian is only supported for cost_types [NON]LINEAR_LS.\n"
+                "GAUSS_NEWTON hessian is not defined for EXTERNAL cost formulation.\n"
                 "If you continue, acados will proceed computing the exact hessian for the cost term.\n"
                 "Note: There is also the option to use the external cost module with a numerical hessian approximation (see `ext_cost_num_hess`).\n"
                 "OR the option to provide a symbolic custom hessian approximation (see `cost_expr_ext_cost_custom_hess`).\n")