added quadrotor

Author: jbcaillau

test/problems/quadrotor.jl

@@ -0,0 +1,54 @@
+# Quadrotor optimal control problem definition used by tests and examples.
+#
+# Returns a NamedTuple with fields:
+#   - ocp  :: the CTParser-defined optimal control problem
+#   - obj  :: reference optimal objective value (Ipopt / MadNLP, Collocation)
+#   - name :: a short problem name
+#   - init :: NamedTuple of components for CTSolvers.initial_guess
+function Quadrotor(; T=1, g=9.8, r=0.1)
+
+    ocp = @def begin
+        t ∈ [0, T], time
+        x ∈ R⁹, state
+        u ∈ R⁴, control
+
+        x(0) == zeros(9)
+
+        ∂(x₁)(t) == x₂(t)
+        ∂(x₂)(t) ==
+        u₁(t) * cos(x₇(t)) * sin(x₈(t)) * cos(x₉(t)) + u₁(t) * sin(x₇(t)) * sin(x₉(t))
+        ∂(x₃)(t) == x₄(t)
+        ∂(x₄)(t) ==
+        u₁(t) * cos(x₇(t)) * sin(x₈(t)) * sin(x₉(t)) - u₁(t) * sin(x₇(t)) * cos(x₉(t))
+        ∂(x₅)(t) == x₆(t)
+        ∂(x₆)(t) == u₁(t) * cos(x₇(t)) * cos(x₈(t)) - g
+        ∂(x₇)(t) == u₂(t) * cos(x₇(t)) / cos(x₈(t)) + u₃(t) * sin(x₇(t)) / cos(x₈(t))
+        ∂(x₈)(t) == -u₂(t) * sin(x₇(t)) + u₃(t) * cos(x₇(t))
+        ∂(x₉)(t) ==
+        u₂(t) * cos(x₇(t)) * tan(x₈(t)) + u₃(t) * sin(x₇(t)) * tan(x₈(t)) + u₄(t)
+
+        dt1 = sin(2π * t / T)
+        df1 = 0
+        dt3 = 2sin(4π * t / T)
+        df3 = 0
+        dt5 = 2t / T
+        df5 = 2
+
+        0.5∫(
+            (x₁(t) - dt1)^2 +
+            (x₃(t) - dt3)^2 +
+            (x₅(t) - dt5)^2 +
+            x₇(t)^2 +
+            x₈(t)^2 +
+            x₉(t)^2 +
+            r * (u₁(t)^2 + u₂(t)^2 + u₃(t)^2 + u₄(t)^2),
+        ) → min
+    end
+
+    init = @init ocp begin
+        x(t) := 0.1 * ones(9) 
+        u(t) := 0.1 * ones(4) 
+    end
+
+    return (ocp=ocp, obj=4.2679623758, name="quadrotor", init=init)
+end