using Convex, SCS, Gadfly # Some constraints on our motion # The object should start from the origin, and end at rest initial_velocity = [-20; 100] final_position = [100; 100] T = 100 # The number of timesteps h = 0.1 # The time between time intervals mass = 1 # Mass of object drag = 0.1 # Drag on object g = [0, -9.8] # Gravity on object # Declare the variables we need position = Variable(2, T) velocity = Variable(2, T) force = Variable(2, T - 1) # Create a problem instance mu = 1 constraints = [] # Add constraints on our variables for i in 1 : T - 1 constraints += position[:, i + 1] == position[:, i] + h * velocity[:, i] end for i in 1 : T - 1 acceleration = force[:, i]/mass + g - drag * velocity[:, i] constraints += velocity[:, i + 1] == velocity[:, i] + h * acceleration end # Add position constraints constraints += position[:, 1] == 0 constraints += position[:, T] == final_position # Add velocity constraints constraints += velocity[:, 1] == initial_velocity constraints += velocity[:, T] == 0 # Solve the problem problem = minimize(sumsquares(force), constraints) solve!(problem, SCSSolver(verbose=0)) pos = evaluate(position) p = plot( layer(x=[pos[1, 1]], y=[pos[2, 1]], Geom.point, Theme(default_color=color("blue"))), layer(x=[pos[1, T]], y=[pos[2, T]], Geom.point, Theme(default_color=color("green"))), layer(x=pos[1, :], y=pos[2, :], Geom.line(preserve_order=true)), Theme(panel_fill=color("white")) ) p = plot(x=1:T, y=sum(evaluate(force).^2, 1), Geom.line, Theme(panel_fill=color("white")))