Add obstacles tutorial

docs/src/tutorials/Systems and Control/obstacles.jl

@@ -0,0 +1,43 @@
+import Pajarito
+using JuMP
+using DynamicPolynomials
+
+model = SOSModel(Pajarito.Optimizer)
+
+@polyvar(t)
+monos = monomials([t], 0:r)
+
+struct Box
+    xl::Float64
+    yl::Float64
+    xu::Float64
+    yu::Float64
+end
+
+boxes = [
+    Box(0, 10, 6, 11),
+    Box(0,  9, 3, 10),
+]
+
+N = 10
+
+T = 1:(N+1)
+
+@variable(model, H[1:N, boxes], Bin)
+
+Mxl = Myl = -20
+Mxu = Myu = 20
+
+p = Dict()
+for j in 1:N
+    @constraint(model, sum(H[j, box] for box in boxes) == 1)
+    p[(:x,j)] = @variable(model, variable_type=Poly(monos))
+    p[(:y,j)] = @variable(model, variable_type=Poly(monos))
+    for box in boxes
+        xl, xu, yl, yu = box.xl, box.xu, box.yl, box.yu
+        @constraint(model, p[(:x,j)] >= Mxl + (xl-Mxl)*H[j,box], domain = (t >= T[j] && t <= T[j+1]))
+        @constraint(model, p[(:x,j)] <= Mxu + (xu-Mxu)*H[j,box], domain = (t >= T[j] && t <= T[j+1]))
+        @constraint(model, p[(:y,j)] >= Myl + (yl-Myl)*H[j,box], domain = (t >= T[j] && t <= T[j+1]))
+        @constraint(model, p[(:y,j)] <= Myu + (yu-Myu)*H[j,box], domain = (t >= T[j] && t <= T[j+1]))
+    end
+end