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Platoon_PF.m
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Platoon_PF.m
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%% Code for the paper
% Title: Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies
% Authors: Zheng, Yang, Shengbo Eben Li, Keqiang Li, Francesco Borrelli, and J. Karl Hedrick.
% Journal: IEEE Transactions on Control Systems Technology 25, no. 3 (2017): 899-910.
%% DMPC for platoons with PF topology
clc;clear;close all;
load PlatoonParameter.mat % This set of parameters was used in the paper
%% Initial Virables
Postion = zeros(Num_step,Num_veh); % postion of each vehicle;
Velocity = zeros(Num_step,Num_veh); % velocity of each vehicle;
Torque = zeros(Num_step,Num_veh); % Braking or Tracking Torque of each vehicle;
U = zeros(Num_step,Num_veh); % Desired Braking or Tracking Torque of each vehicle;
Cost = zeros(Num_step,Num_veh); % Cost function
Exitflg = zeros(Num_step,Num_veh); % Stop flag - solvers
% Leading vehicle
d = 20; % Desired spacing
a0 = zeros(Num_step,1);
v0 = zeros(Num_step,1);
x0 = zeros(Num_step,1);
% Transient process of leader, which is given in advance
v0(1) = 20; a0(1/Tim_step+1:2/Tim_step) = 2;
for i = 2:Num_step
v0(i) = v0(i-1)+a0(i)*Tim_step;
x0(i) = x0(i-1)+v0(i)*Tim_step;
end
% Zero initial error for the followers
for i = 1:Num_veh
Postion(1,i) = x0(1)-i*d;
Velocity(1,i) = 20;
Torque(1,i) = (Mass(i)*g*f + Ca(i)*Velocity(1,i)^2)*R(i)/Eta;
end
%% MPC weighted matrix in the cost function
% PF topology --> Fi > Gi+1
% Q1 : leader weighted matrix for state;
% R1 --> leader weighted matrix for control input
% Fi --> penalty for deviation of its own assumed trajectory
% Gi --> penalty for deviation of its neighbors' assumed trajectory
F1 = 10*eye(2); G1 = 0; Q1 = 10*eye(2);R1 = 1;
F2 = 10*eye(2); G2 = 5*eye(2);Q2 = 0*eye(2); R2 = 1;
F3 = 10*eye(2); G3 = 5*eye(2);Q3 = 0*eye(2); R3 = 1;
F4 = 10*eye(2); G4 = 5*eye(2);Q4 = 0*eye(2); R4 = 1;
F5 = 10*eye(2); G5 = 5*eye(2);Q5 = 0*eye(2); R5 = 1;
F6 = 10*eye(2); G6 = 5*eye(2);Q6 = 0*eye(2); R6 = 1;
F7 = 10*eye(2); G7 = 5*eye(2);Q7 = 0*eye(2); R7 = 1;
% Distributed MPC assumed state
Np = 20; % Predictive horizon
Pa = zeros(Np,Num_veh); % Assumed postion of each vehicle;
Va = zeros(Np,Num_veh); % Assumed velocity of each vehicle;
ua = zeros(Np,Num_veh); % Assumed Braking or Tracking Torque input of each vehicle;
Pa_next = zeros(Np+1,Num_veh); % 1(0): Assumed postion of each vehicle at the newt time step;
Va_next = zeros(Np+1,Num_veh); % Assumed velocity of each vehicle at the newt time step;
ua_next = zeros(Np+1,Num_veh); % Assumed Braking or Tracking Torque of each vehicle at the newt time step;
% Initialzie the assumed state for the first computation: constant speed
for i = 1:Num_veh
ua(:,i) = Torque(1,i);
Pa(1,i) = Postion(1,i); % The first point should be interpreted as k = 0 (current state)
Va(1,i) = Velocity(1,i);
Ta(1,i) = Torque(1,i);
for j = 1:Np
[Pa(j+1,i),Va(j+1,i),Ta(j+1,i)] = VehicleDynamic(ua(j,i),Tim_step,Pa(j,i),Va(j,i),Ta(j,i),Mass(i),R(i),g,f,Eta,Ca(i),Tao(i));
end
end
tol_opt = 1e-5;
options = optimset('Display','off','TolFun', tol_opt, 'MaxIter', 2000,...
'LargeScale', 'off', 'RelLineSrchBnd', [], 'RelLineSrchBndDuration', 1);
%% For debugging
% Terminal state
Xend = zeros(Num_step,Num_veh); Vend = zeros(Num_step,Num_veh);
%% Iterative Simulation
for i = 2:Num_step - Np
fprintf('\n Steps i= %d\n',i)
% Solve optimization problem
tic
%% Vehicle one
Vehicle_Type = [Mass(1),R(1),g,f,Eta,Ca(1),Tao(1)]; % the vehicle parameters ： Mass,R,g,f,Eta,Ca(i),Tao,
X0 = [Postion(i-1,1),Velocity(i-1,1),Torque(i-1,1)]; % the vehicle variable in the last time step
Pd = x0(i-1:i+Np-1) - d; Vd = v0(i-1:i+Np-1); % Np+1 points in total: i-1 last state， i to be optimized
Xdes = [Pd,Vd]; % Desired state of the first vehicle
Xa = [Pa(:,1),Va(:,1)]; % Assumed state, which is passed to the next vehicle
Xnba = zeros(Np+1,2); % 1：last state
u0 = ua(:,1); % initial searching point
A = [];b = []; Aeq = []; beq = []; % no linear constraints
lb = Torquebound(1,1)*ones(Np,1); ub = Torquebound(1,2)*ones(Np,1); % upper and lower bound for input
Pnp = Pd(end,1); Vnp = Vd(end,1); % Terminal constraints
Xend(i,1) = Pnp; Vend(i,1) = Vnp; Tnp = (Ca(1)*Vnp.^2 + Mass(1)*g*f)/Eta*R(1);
% MPC - subproblem in vehicle 1
[u, Cost(i,1), Exitflg(i,1), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q1,Xdes,R1,F1,Xa,G1,Xnba), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,1) = u(1);
[Postion(i,1),Velocity(i,1),Torque(i,1)] = VehicleDynamic(U(i,1),Tim_step,Postion(i-1,1),Velocity(i-1,1),Torque(i-1,1),Mass(1),R(1),g,f,Eta,Ca(1),Tao(1));
% Update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,1),Velocity(i,1),Torque(i,1)];
ua(1:Np-1,1) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,1),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(1),R(1),g,f,Eta,Ca(1),Tao(1));
end
ua(Np,1) = (Ca(1)*Temp(Np,2).^2 + Mass(1)*g*f)/Eta*R(1);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,1),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(1),R(1),g,f,Eta,Ca(1),Tao(1));
Pa_next(:,1) = Temp(:,1);
Va_next(:,1) = Temp(:,2);
toc
%% Vehicle two
tic
Vehicle_Type = [Mass(2),R(2),g,f,Eta,Ca(2),Tao(2)]; % the vehicle parameters ： Mass,R,g,f,Eta,Ca(i),Tao,
X0 = [Postion(i-1,2),Velocity(i-1,2),Torque(i-1,2)]; % the vehicle variable in the last time
Pd = zeros(Np+1,1); Vd = zeros(Np+1,1);
Xdes = [Pd,Vd];
Xa = [Pa(:,2),Va(:,2)];
Xnfa = [Pa(:,1) - d, Va(:,1)];
u0 = ua(:,2);
A = [];b = []; Aeq = []; beq = [];
lb = Torquebound(2,1)*ones(Np,1); ub = Torquebound(2,2)*ones(Np,1);
Pnp = Xnfa(end,1); Vnp = Xnfa(end,2);
Xend(i,2) = Pnp; Vend(i,2) = Vnp; Tnp = (Ca(2)*Vnp.^2 + Mass(2)*g*f)/Eta*R(2);
% MPC - subporblem for vehicle 2
[u, Cost(i,2), Exitflg(i,2), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q2,Xdes,R2,F2,Xa,G2,Xnfa), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,2) = u(1);
[Postion(i,2),Velocity(i,2),Torque(i,2)] = VehicleDynamic(U(i,2),Tim_step,Postion(i-1,2),Velocity(i-1,2),Torque(i-1,2),Mass(2),R(2),g,f,Eta,Ca(2),Tao(2));
% Update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,2),Velocity(i,2),Torque(i,2)];
ua(1:Np-1,2) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,2),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(2),R(2),g,f,Eta,Ca(2),Tao(2));
end
ua(Np,2) = (Ca(2)*Temp(Np,2).^2 + Mass(2)*g*f)/Eta*R(2);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,2),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(2),R(2),g,f,Eta,Ca(2),Tao(2));
Pa_next(:,2) = Temp(:,1);
Va_next(:,2) = Temp(:,2);
toc
%% vehicle three
tic
Vehicle_Type = [Mass(3),R(3),g,f,Eta,Ca(3),Tao(3)]; % the vehicle parameters ： Mass,R,g,f,Eta,Ca(i),Tao,
X0 = [Postion(i-1,3),Velocity(i-1,3),Torque(i-1,3)]; % the vehicle variable in the last time
Pd = zeros(Np+1,1); Vd = zeros(Np+1,1);
Xdes = [Pd,Vd];
Xa = [Pa(:,3),Va(:,3)];
Xnfa = [Pa(:,2) - d, Va(:,2)];
u0 = ua(:,3);
A = [];b = []; Aeq = []; beq = [];
lb = Torquebound(3,1)*ones(Np,1); ub = Torquebound(3,2)*ones(Np,1);
Pnp = Xnfa(end,1); Vnp = Xnfa(end,2);
Xend(i,3) = Pnp; Vend(i,3) = Vnp; Tnp = (Ca(3)*Vnp.^2 + Mass(3)*g*f)/Eta*R(3);
% MPC-subproblem
[u, Cost(i,3), Exitflg(i,3), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q3,Xdes,R3,F3,Xa,G3,Xnfa), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,3) = u(1);
[Postion(i,3),Velocity(i,3),Torque(i,3)] = VehicleDynamic(U(i,3),Tim_step,Postion(i-1,3),Velocity(i-1,3),Torque(i-1,3),Mass(3),R(3),g,f,Eta,Ca(3),Tao(3));
% update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,3),Velocity(i,3),Torque(i,3)];
ua(1:Np-1,3) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,3),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(3),R(3),g,f,Eta,Ca(3),Tao(3));
end
ua(Np,3) = (Ca(3)*Temp(Np,2).^2 + Mass(3)*g*f)/Eta*R(3);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,3),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(3),R(3),g,f,Eta,Ca(3),Tao(3));
Pa_next(:,3) = Temp(:,1);
Va_next(:,3) = Temp(:,2);
toc
%% vehicle four
tic
Vehicle_Type = [Mass(4),R(4),g,f,Eta,Ca(4),Tao(4)]; % the vehicle parameters ： Mass,R,g,f,Eta,Ca(i),Tao,
X0 = [Postion(i-1,4),Velocity(i-1,4),Torque(i-1,4)];
Pd = zeros(Np+1,1); Vd = zeros(Np+1,1);
Xdes = [Pd,Vd];
Xa = [Pa(:,4),Va(:,4)];
Xnfa = [Pa(:,3) - d, Va(:,3)];
u0 = ua(:,4);
A = [];b = []; Aeq = []; beq = [];
lb = Torquebound(4,1)*ones(Np,1); ub = Torquebound(4,2)*ones(Np,1);
Pnp = Xnfa(end,1); Vnp = Xnfa(end,2);
Xend(i,4) = Pnp; Vend(i,4) = Vnp; Tnp = (Ca(4)*Vnp.^2 + Mass(4)*g*f)/Eta*R(4);
% MPC-subproblem
[u, Cost(i,4), Exitflg(i,4), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q3,Xdes,R3,F3,Xa,G3,Xnfa), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,4) = u(1);
[Postion(i,4),Velocity(i,4),Torque(i,4)] = VehicleDynamic(U(i,4),Tim_step,Postion(i-1,4),Velocity(i-1,4),Torque(i-1,4),Mass(4),R(4),g,f,Eta,Ca(4),Tao(4));
% Update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,4),Velocity(i,4),Torque(i,4)];
ua(1:Np-1,4) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,4),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(4),R(4),g,f,Eta,Ca(4),Tao(4));
end
ua(Np,4) = (Ca(4)*Temp(Np,2).^2 + Mass(4)*g*f)/Eta*R(4);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,4),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(4),R(4),g,f,Eta,Ca(4),Tao(4));
Pa_next(:,4) = Temp(:,1);
Va_next(:,4) = Temp(:,2);
toc
%% vehicle five
tic
Vehicle_Type = [Mass(5),R(5),g,f,Eta,Ca(5),Tao(5)];
X0 = [Postion(i-1,5),Velocity(i-1,5),Torque(i-1,5)];
Pd = zeros(Np+1,1); Vd = zeros(Np+1,1);
Xdes = [Pd,Vd]; % Udes = Td;
Xa = [Pa(:,5),Va(:,5)];
Xnfa = [Pa(:,4) - d, Va(:,4)];
u0 = ua(:,5);
A = [];b = []; Aeq = []; beq = [];
lb = Torquebound(5,1)*ones(Np,1); ub = Torquebound(5,2)*ones(Np,1);
Pnp = Xnfa(end,1); Vnp = Xnfa(end,2);
Xend(i,5) = Pnp; Vend(i,5) = Vnp; Tnp = (Ca(5)*Vnp.^2 + Mass(5)*g*f)/Eta*R(5);
% MPC -subproblem
[u, Cost(i,5), Exitflg(i,5), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q3,Xdes,R3,F3,Xa,G3,Xnfa), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,5) = u(1);
[Postion(i,5),Velocity(i,5),Torque(i,5)] = VehicleDynamic(U(i,5),Tim_step,Postion(i-1,5),Velocity(i-1,5),Torque(i-1,5),Mass(5),R(5),g,f,Eta,Ca(5),Tao(5));
% update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,5),Velocity(i,5),Torque(i,5)];
ua(1:Np-1,5) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,5),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(5),R(5),g,f,Eta,Ca(5),Tao(5));
end
ua(Np,5) = (Ca(5)*Temp(Np,2).^2 + Mass(5)*g*f)/Eta*R(5);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,5),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(5),R(5),g,f,Eta,Ca(5),Tao(5));
Pa_next(:,5) = Temp(:,1);
Va_next(:,5) = Temp(:,2);
toc
%% vehicle six
tic
Vehicle_Type = [Mass(6),R(6),g,f,Eta,Ca(6),Tao(6)]; % the vehicle parameters ： Mass,R,g,f,Eta,Ca(i),Tao,
X0 = [Postion(i-1,6),Velocity(i-1,6),Torque(i-1,6)]; % the vehicle variable in the last time
Pd = zeros(Np+1,1); Vd = zeros(Np+1,1);
Xdes = [Pd,Vd];
Xa = [Pa(:,6),Va(:,6)];
Xnfa = [Pa(:,5) - d, Va(:,5)];
u0 = ua(:,6);
A = [];b = []; Aeq = []; beq = [];
lb = Torquebound(6,1)*ones(Np,1); ub = Torquebound(6,2)*ones(Np,1);
Pnp = Xnfa(end,1); Vnp = Xnfa(end,2);
Xend(i,6) = Pnp; Vend(i,6) = Vnp; Tnp = (Ca(6)*Vnp.^2 + Mass(6)*g*f)/Eta*R(6);
% MPC 优化求解
[u, Cost(i,6), Exitflg(i,6), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q3,Xdes,R3,F3,Xa,G3,Xnfa), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,6) = u(1);
[Postion(i,6),Velocity(i,6),Torque(i,6)] = VehicleDynamic(U(i,6),Tim_step,Postion(i-1,6),Velocity(i-1,6),Torque(i-1,6),Mass(6),R(6),g,f,Eta,Ca(6),Tao(6));
% update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,6),Velocity(i,6),Torque(i,6)];
ua(1:Np-1,6) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,6),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(6),R(6),g,f,Eta,Ca(6),Tao(6));
end
ua(Np,6) = (Ca(6)*Temp(Np,2).^2 + Mass(6)*g*f)/Eta*R(6);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,6),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(6),R(6),g,f,Eta,Ca(6),Tao(6));
Pa_next(:,6) = Temp(:,1);
Va_next(:,6) = Temp(:,2);
toc
%% vehicle seven
tic
Vehicle_Type = [Mass(7),R(7),g,f,Eta,Ca(7),Tao(7)]; % the vehicle parameters ： Mass,R,g,f,Eta,Ca(i),Tao,
X0 = [Postion(i-1,7),Velocity(i-1,7),Torque(i-1,7)]; % the vehicle variable in the last time
Pd = zeros(Np+1,1); Vd = zeros(Np+1,1);
Xdes = [Pd,Vd]; % Udes = Td;
Xa = [Pa(:,7),Va(:,7)];
Xnfa = [Pa(:,6) - d, Va(:,6)];
u0 = ua(:,7);
A = [];b = []; Aeq = []; beq = [];
lb = Torquebound(7,1)*ones(Np,1); ub = Torquebound(7,2)*ones(Np,1);
Pnp = Xnfa(end,1); Vnp = Xnfa(end,2);
Xend(i,7) = Pnp; Vend(i,7) = Vnp; Tnp = (Ca(7)*Vnp.^2 + Mass(7)*g*f)/Eta*R(7);
% MPC-subproblem
[u, Cost(i,7), Exitflg(i,7), output] = fmincon(@(u) Costfunction2( Np, Tim_step, X0 ,u, Vehicle_Type,Q3,Xdes,R3,F3,Xa,G3,Xnfa), ...
u0, A, b, Aeq, beq, lb, ub, @(u) Nonlinearconstraints(Np, Tim_step, X0, u, Vehicle_Type,Pnp,Vnp,Tnp),options);
% state involves one step
U(i,7) = u(1);
[Postion(i,7),Velocity(i,7),Torque(i,7)] = VehicleDynamic(U(i,7),Tim_step,Postion(i-1,7),Velocity(i-1,7),Torque(i-1,7),Mass(7),R(7),g,f,Eta,Ca(7),Tao(7));
% update assumed state
Temp = zeros(Np+1,3);
Temp(1,:) = [Postion(i,7),Velocity(i,7),Torque(i,7)];
ua(1:Np-1,7) = u(2:Np);
for j = 1:Np-1
[Temp(j+1,1),Temp(j+1,2),Temp(j+1,3)] = VehicleDynamic(ua(j,7),Tim_step,Temp(j,1),Temp(j,2),Temp(j,3),Mass(7),R(7),g,f,Eta,Ca(7),Tao(7));
end
ua(Np,7) = (Ca(7)*Temp(Np,2).^2 + Mass(7)*g*f)/Eta*R(7);
[Temp(Np+1,1),Temp(Np+1,2),Temp(Np+1,3)] = VehicleDynamic(ua(Np,7),Tim_step,Temp(Np,1),Temp(Np,2),Temp(Np,3),Mass(7),R(7),g,f,Eta,Ca(7),Tao(7));
Pa_next(:,7) = Temp(:,1);
Va_next(:,7) = Temp(:,2);
toc
%% Update assumed data
Pa = Pa_next;
Va = Va_next;
end
FigurePlot