Failures due to tangent in nonlinear constraint, and Couenne error

[jelavice]

first version of model with tangent

using JuMP
using CoinOptServices
dt = 0.10;        # sampling time
L = 1; 
g = 9.81;
mu = 0.8;
N = 5 # prediction horizont
mdl = Model(solver = OsilCouenneSolver())
err = 0;
δ_traj = zeros(N);
a_traj = zeros(N);
x_traj = zeros(N+1);
y_traj = zeros(N+1);
ψ_traj = zeros(N+1);
v_traj = zeros(N+1);
errLateral = minimum([err 0.2]);
rateLimits = [20*pi/180, 10];
δ_old = 0;
a_old = 0;
@defNLParam(mdl, δ_ref[i=1:N] == δ_traj[i])
@defNLParam(mdl, a_ref[i=1:N] == a_traj[i])
@defNLParam(mdl, x_ref[i=1:(N+1)] == x_traj[i])
@defNLParam(mdl, y_ref[i=1:(N+1)] == y_traj[i])
@defNLParam(mdl, ψ_ref[i=1:(N+1)] == ψ_traj[i])
@defNLParam(mdl, v_ref[i=1:(N+1)] == v_traj[i])
@defNLParam(mdl, D == errLateral)
@defVar(mdl, x[1:(N+1)])
@defVar(mdl, y[1:(N+1)])
@defVar(mdl, ψ[1:(N+1)])
@defVar(mdl, v[1:(N+1)])
@defVar(mdl, δ[1:N])
@defVar(mdl, a[1:N])
@defVar(mdl, p[1:3], Bin)
Q = eye(4);
R = eye(2);
@setNLObjective(mdl, Min, sum{ Q[1,1]*(x[i] - x_ref[i])^2 + Q[2,2]*(y[i] - y_ref[i])^2 + Q[3,3]*(ψ[i] - ψ_ref[i])^2 + Q[4,4]*(v[i] - v_ref[i])^2, i = 2:N} + 
                          sum{100*(ψ[i+1] - ψ[i])^2 ,i=1:N} +
                          sum{ R[1,1]*(δ[i] - δ_ref[i])^2 + R[1,1]*(a[i] - a_ref[i])^2 , i=1:N} +
                          Q[1,1]*(x[N+1] - x_ref[N+1])^2 + Q[2,2]*(y[N+1] - y_ref[N+1])^2 + Q[3,3]*(ψ[N+1] - ψ_ref[N+1])^2 + Q[4,4]*(v[N+1] - v_ref[N+1])^2 );
x0 = 0;
y0 = 0;
ψ0 = 0;
v0 = 0;
@addNLConstraint(mdl, x[1] == x0)
@addNLConstraint(mdl, y[1] == y0)
@addNLConstraint(mdl, ψ[1] == ψ0)
@addNLConstraint(mdl, v[1] == v0)
@addNLConstraint(mdl,  abs(δ[1] - δ_old) <= rateLimits[1]*dt);
@addNLConstraint(mdl,  abs(a[1] - a_old) <= rateLimits[2]*dt);
for i = 1:N
    @addNLConstraint(mdl, x[i+1] == x[i] +dt*v[i]*cos(ψ[i]));       
    @addNLConstraint(mdl, y[i+1] == y[i] +dt*v[i]*sin(ψ[i]));       
    @addNLConstraint(mdl, ψ[i+1] == ψ[i] +dt*v[i]*tan(δ[i])/L); # CHANGEME
#    @addNLConstraint(mdl, ψ[i+1] == ψ[i] +dt*v[i]*sin(δ[i])/(L*cos(δ[i])));  
    @addNLConstraint(mdl, x[i+1] == v[i] +dt*a[i]); 
    @addNLConstraint(mdl, abs(δ[i]) <= 30*pi/180);       
    @addNLConstraint(mdl, abs(a[i]) <= mu*g/4);     
    if i < N
        @addNLConstraint(mdl, abs(δ[i+1] - δ[i]) <= rateLimits[1]*dt);
        @addNLConstraint(mdl, abs(a[i+1] - a[i]) <= rateLimits[1]*dt);
    end
    @addNLConstraint(mdl, abs(ψ[i] - ψ_ref[i])  <= 45*pi/180 );
    if i <= N
        @addNLConstraint(mdl, abs(ψ[i+1] - ψ[i])  <= dt*30*pi/180);
    end
end
for i=1:3
    @addNLConstraint(mdl, p[i]*( (x[N+1] - x_ref[(N+1)-i+1])^2 + (y[N+1] - y_ref[(N+1)-i+1])^2 ) <= D^2);
    @addNLConstraint(mdl, p[i]*(abs(ψ[N+1] - ψ_ref[(N+1)-i+1])) <= 5*pi/180);                 
end             
@addNLConstraint(mdl, sum{p[i] ,i=1:3} >= 1);
solve(mdl)

This is using Julia 0.4.3 on 32 bit Windows. With tan in the constraint line that says # CHANGEME this gives an error from OSSolverService:

<message>encountered a spurious character in the lexer
The first character is: <
See line number: 546

Replacing the tan with sin/cos results in Couenne exiting. OsilBonminSolver and CouenneNLSolver both work fine here.

[tkelman]

Thanks Edo. 3e072fe works around the issue with tangent, giving a more sane Julia error message for now. The underlying solvers seem able to handle tangent since AmplNLWriter works, so I should probably report this along with the Couenne exiting issue to the upstream Optimization Services developers if I can reproduce on their latest version.