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Copy pathCLF_CBF_QP.m
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CLF_CBF_QP.m
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classdef CLF_CBF_QP
properties
param_opt; % qp relevant parameters
param_sys; % parameters of vehicles
goal; % control objective
straightlane; % driving lanes
other_vehicles; % surrounding vehicles
end
methods
function self = CLF_CBF_QP(cbf_param, veh_param, controller_goal, straightlane, other_vehicles)
self.param_opt = cbf_param;
self.param_sys = veh_param;
self.goal = controller_goal;
self.straightlane = straightlane;
self.other_vehicles = other_vehicles;
end
function [acc_flag, input, e] = get_optimal_input(self, state, last_input, lane_id, input_log, current_lane_id, direction_flag, acc_flag)
%% load parameter and control objective
safety_factor = self.goal.safety_factor;
lim_speed = self.goal.lim_speed;
l_rc = self.param_sys.l_rc;
l_fc = self.param_sys.l_fc;
l_f = self.param_sys.l_f;
l_r = self.param_sys.l_r;
width = self.param_sys.width;
dt = self.param_opt.dt;
[x, y, psi, v] = self.unpack_state(state);
[acc, beta] = self.unpack_input(last_input);
alpha_y = self.param_opt.alpha_y;
alpha_v = self.param_opt.alpha_v;
alpha_yaw = self.param_opt.alpha_yaw;
gamma_1 = self.param_opt.gamma_1;
gamma_2 = self.param_opt.gamma_2;
gamma_3 = self.param_opt.gamma_3;
gamma_4 = self.param_opt.gamma_4;
gamma_5 = self.param_opt.gamma_5;
gamma_6 = self.param_opt.gamma_6;
target_y = self.goal.target_y;
%% load surrounding vehicles
current_lane_vehicles = [];
target_lane_vehicles = [];
num_veh = length(self.other_vehicles);
% sort surrounding vehilces according to the lane id information
for i = 1:num_veh
if (self.other_vehicles(i).lane_id == current_lane_id | self.other_vehicles(i).lane_id == current_lane_id - direction_flag * 0.5)
% the vehicle is in the current lane
if self.other_vehicles(i).state(1) >= x
% collect the vehicle in the current lane before the
% ego vehicle
current_lane_vehicles = [current_lane_vehicles, self.other_vehicles(i)];
end
elseif self.other_vehicles(i).lane_id == current_lane_id + direction_flag * 0.5
% the vehicle is accross the dividing line
if self.other_vehicles(i).state(1) >= x
current_lane_vehicles = [current_lane_vehicles, self.other_vehicles(i)];
end
target_lane_vehicles = [target_lane_vehicles, self.other_vehicles(i)];
elseif (self.other_vehicles(i).lane_id == current_lane_id + direction_flag)
target_lane_vehicles = [target_lane_vehicles, self.other_vehicles(i)];
elseif self.other_vehicles(i).lane_id == current_lane_id + 1.5 * direction_flag
target_lane_vehicles = [target_lane_vehicles, self.other_vehicles(i)];
end
end
car_fc = []; % car_fc is the closest leading vehicle in the current lane (vehicle fc)
carfc_range = x + 100; % this value can be tuned, it shows in which range the vehicle would be considered
for j = 1:length(current_lane_vehicles)
if current_lane_vehicles(j).state(1) <= carfc_range
car_fc = current_lane_vehicles(j);
carfc_range = current_lane_vehicles(j).state(1);
end
end
car_bt = []; % car_bt is the closeset vehicle in the target lane that is behind ego vehicle (vehicle bt)
car_bt_range = x - 100;
car_ft = []; % car_ft is the closet leading vehicle in the target lane (vehicle ft)
carft_range = x + 100;
for i = 1:length(target_lane_vehicles)
if target_lane_vehicles(i).state(1) <= x & target_lane_vehicles(i).state(1) >= car_bt_range
car_bt = target_lane_vehicles(i);
car_bt_range = target_lane_vehicles(i).state(1);
end
if target_lane_vehicles(i).state(1) >= x & target_lane_vehicles(i).state(1) <= carft_range
car_ft = target_lane_vehicles(i);
carft_range = target_lane_vehicles(i).state(1);
end
end
if lane_id == current_lane_id + direction_flag
acc_flag = 0; % indicates if ego vehicle is accelerating
end
if acc_flag == 0
target_speed = self.goal.target_speed;
else
target_speed = lim_speed;
end
%% CLF-CBF-QP formulation
%% lateral position CLF
h_y = y - target_y;
V_y = h_y^2;
phi0_y = 2 * h_y * (v * sin(psi)) + alpha_y * V_y;
phi1_y = [0, 2 * h_y * v * cos(psi)];
%% velocity CLF
h_v = v - target_speed;
V_v = h_v^2;
phi0_v = alpha_v * V_v;
phi1_v = [2 * h_v * 1, 0];
%% yaw angle CLF
h_yaw = psi;
V_yaw = h_yaw^2;
phi0_yaw = alpha_yaw * V_yaw;
phi1_yaw = [0, 2 * h_yaw * v * l_r];
Aclf = [phi1_y, -1, 0, 0; ...
phi1_v, 0, -1, 0; ...
phi1_yaw, 0, 0, -1;];
bclf = [-phi0_y; -phi0_v; -phi0_yaw];
%% Car_fc relevant CBFs
if isempty(car_fc)
Acbf1 = [0, 0, 0, 0, 0];
bcbf1 = [0];
Acbf2 = [0, 0, 0, 0, 0];
bcbf2 = [0];
h_CBF1 = [];
h_CBF2 = [];
else
x_carfc_rear = car_fc.state(1) - l_rc;
v_carfc = car_fc.state_log(4, end);
a_carfc = car_fc.input(1);
% distance based CBF
h_CBF1 = x_carfc_rear - x - self.param_sys.l_fc;
h1dot = v_carfc;
Lfh1 = [-cos(psi) * v];
Lgh1 = [0, v * sin(psi)];
Acbf1 = [-Lgh1, 0, 0, 0];
bcbf1 = [Lfh1 + gamma_1 * h_CBF1 + h1dot];
% force based CBF
if v > v_carfc
h_CBF2 = x_carfc_rear - x - self.param_sys.l_fc - (1 + safety_factor) * v - 0.5 * (v_carfc - v) * (v_carfc - v) / self.goal.lim_acc;
h2dot = v_carfc - (0.5 / self.goal.lim_acc) * 2 * (v_carfc - v) * a_carfc;
Lfh2 = [-cos(psi) * v];
Lgh2 = [(-(1 + safety_factor) + (v_carfc - v) / self.goal.lim_acc), v * sin(psi)];
Acbf2 = [-Lgh2, 0, 0, 0];
bcbf2 = [Lfh2 + gamma_2 * h_CBF2 + h2dot];
else
h_CBF2 = x_carfc_rear - x - self.param_sys.l_fc - (1 + safety_factor) * v;
h2dot = v_carfc;
Lfh2 = [-cos(psi) * v];
Lgh2 = [-(1 + safety_factor), v * sin(psi)];
Acbf2 = [-Lgh2, 0, 0, 0];
bcbf2 = [Lfh2 + gamma_2 * h_CBF2 + h2dot];
end
end
%% Car_bt relevant CBFs
if isempty(car_bt)
Acbf3 = [0, 0, 0, 0, 0];
bcbf3 = [0];
Acbf4 = [0, 0, 0, 0, 0];
bcbf4 = [0];
h_CBF3 = [];
h_CBF4 = [];
else
x_carbt_front = car_bt.state(1) + l_fc;
v_carbt = car_bt.state_log(4, end);
a_carbt = car_bt.input(1);
if car_bt.state(1) <= x - l_fc - l_rc
% distance based CBF
if v_carbt <= v
h_CBF3 = x - l_rc - x_carbt_front;
h3dot = -v_carbt;
Lfh3 = (cos(psi) * v);
Lgh3 = [0, -v * sin(psi)];
Acbf3 = [-Lgh3, 0, 0, 0];
bcbf3 = [Lfh3 + gamma_3 * h_CBF3 + h3dot];
else
h_CBF3 = x - l_rc - x_carbt_front - 0.5 * (v_carbt - v) * (v_carbt - v) / self.goal.lim_acc;
h3dot = -v_carbt - (1 / self.goal.lim_acc) * (v_carbt - v) * a_carbt;
Lfh3 = (cos(psi) * v);
Lgh3 = [(v - v_carbt) / self.goal.lim_acc, -v * sin(psi)];
Acbf3 = [-Lgh3, 0, 0, 0];
bcbf3 = [Lfh3 + gamma_3 * h_CBF3 + h3dot];
end
else
h_CBF3 = direction_flag * (car_bt.state(2) - y - width - safety_factor);
Lfh3 = -direction_flag * v * sin(psi);
Lgh3 = [0, -direction_flag * v * cos(psi)];
Acbf3 = [-Lgh3, 0, 0, 0];
bcbf3 = [Lfh3 + gamma_3 * h_CBF3];
end
if v_carbt > v
h_CBF4 = -x_carbt_front + x - l_rc - (1 + safety_factor) * v_carbt - 0.5 * (v_carbt - v) * (v_carbt - v) / self.goal.lim_acc;
h4dot = -v_carbt - (1 + safety_factor) * a_carbt - (1 / self.goal.lim_acc) * (v_carbt - v) * a_carbt;
Lfh4 = (cos(psi) * v);
Lgh4 = [(v - v_carbt) / self.goal.lim_acc, -v * sin(psi)];
Acbf4 = [-Lgh4, 0, 0, 0];
bcbf4 = [Lfh4 + gamma_4 * h_CBF4 + h4dot];
else
h_CBF4 = -x_carbt_front + x - l_rc - (1 + safety_factor) * v_carbt;
h4dot = -v_carbt - (1 + safety_factor) * car_bt.input(1);
Lfh4 = cos(psi) * v;
Lgh4 = [0, -v * sin(psi)];
Acbf4 = [-Lgh4, 0, 0, 0];
bcbf4 = [Lfh4 + gamma_4 * h_CBF4 + h4dot];
end
end
%% Car_ft relevant CBFs
if isempty(car_ft)
Acbf5 = [0, 0, 0, 0, 0];
bcbf5 = [0];
Acbf6 = [0, 0, 0, 0, 0];
bcbf6 = [0];
h_CBF5 = [];
h_CBF6 = [];
else
x_carft_rear = car_ft.state(1) - l_rc;
v_carft = car_ft.state_log(4, end);
a_carft = car_ft.input_log(1, end);
if car_ft.state(1) - x > l_fc + l_rc
% distance based CBF
if v_carft >= v
h_CBF5 = x_carft_rear - x - self.param_sys.l_fc;
h5dot = v_carft;
Lfh5 = (-cos(psi) * v);
Lgh5 = [0, v * sin(psi)];
Acbf5 = [-Lgh5, 0, 0, 0];
bcbf5 = [Lfh5 + gamma_5 * h_CBF5 + h5dot];
else
h_CBF5 = x_carft_rear - x - self.param_sys.l_fc - 0.5 * (v_carft - v) * (v_carft - v) / self.goal.lim_acc;
h5dot = v_carft - (0.5 / self.goal.lim_acc) * 2 * (v_carft - v) * a_carft;
Lfh5 = (-cos(psi) * v);
Lgh5 = [((v_carft - v) / self.goal.lim_acc), v * sin(psi)];
Acbf5 = [-Lgh5, 0, 0, 0];
bcbf5 = [Lfh5 + gamma_5 * h_CBF5 + h5dot];
end
else
h_CBF5 = direction_flag * (car_ft.state(2) - y - width - safety_factor);
Lfh5 = -direction_flag * v * sin(psi);
Lgh5 = [0, -direction_flag * v * cos(psi)];
Acbf5 = [-Lgh5, 0, 0, 0];
bcbf5 = [Lfh5 + gamma_5 * h_CBF5];
end
% force based CBF
if v_carft < v
h_CBF6 = x_carft_rear - x - self.param_sys.l_fc - (1 + safety_factor) * v - 0.5 * (v_carft - v) * (v_carft - v) / self.goal.lim_acc;
h6dot = v_carft - (0.5 / self.goal.lim_acc) * 2 * (v_carft - v) * a_carft;
Lfh6 = -cos(psi) * v;
Lgh6 = [(-(1 + safety_factor) + (v_carft - v) / self.goal.lim_acc), v * sin(psi)];
Acbf6 = [-Lgh6, 0, 0, 0];
bcbf6 = [Lfh6 + gamma_6 * h_CBF6 + h6dot];
else
h_CBF6 = x_carft_rear - x - self.param_sys.l_fc - (1 + safety_factor) * v;
h6dot = v_carft;
Lfh6 = (-cos(psi) * v);
Lgh6 = [-(1 + safety_factor), v * sin(psi)];
Acbf6 = [-Lgh6, 0, 0, 0];
bcbf6 = [Lfh6 + gamma_6 * h_CBF6 + h6dot];
end
end
% three states, 0: keep the current lane, 1: change to the left
% adjacent lane, -1: change to the right adjacent lane
if direction_flag == 0 % ACC state
% only car_fc relevant CBF is considered
Acbf3 = [0, 0, 0, 0, 0];
bcbf3 = [0];
Acbf4 = [0, 0, 0, 0, 0];
bcbf4 = [0];
Acbf5 = [0, 0, 0, 0, 0];
bcbf5 = [0];
Acbf6 = [0, 0, 0, 0, 0];
bcbf6 = [0];
else % the ego vehicle is changing its lane, L or R state
if lane_id == current_lane_id + direction_flag
% the ego vehicle is already in its target lane, we
% don't need car_fc and car_bt relevant CBFs
Acbf1 = [0, 0, 0, 0, 0];
bcbf1 = [0];
Acbf2 = [0, 0, 0, 0, 0];
bcbf2 = [0];
Acbf3 = [0, 0, 0, 0, 0];
bcbf3 = [0];
Acbf4 = [0, 0, 0, 0, 0];
bcbf4 = [0];
end
end
% input constraint (accleration limit, slip anlge limit,
% lateral acceleration limit, slip angle changing rate limit)
A_u = [1, 0, 0, 0, 0; ...
-1, 0, 0, 0, 0; ...
0, 1, 0, 0, 0; ...
0, -1, 0, 0, 0; ...
cos(psi + beta), 0, 0, 0, 0; ...
-cos(psi + beta), 0, 0, 0, 0];
A_u0 = [0, 1, 0, 0, 0; ...
0, -1, 0, 0, 0];
b_u = [self.goal.lim_acc; self.goal.lim_acc; self.goal.lim_beta; self.goal.lim_beta; 0.5 * 0.9 * 9.81; 0.5 * 0.9 * 9.81];
b_u0 = [beta + 1 * self.goal.lim_slip_rate * dt; -beta + 1 * self.goal.lim_slip_rate * dt];
Constraint_A = [Aclf; Acbf2; Acbf4; Acbf6; A_u; A_u0];
Constraint_b = [bclf; bcbf2; bcbf4; bcbf6; b_u; b_u0];
H = self.param_opt.H;
F = self.param_opt.F;
options = optimoptions('quadprog', 'Display', 'off');
u = quadprog(H, F, Constraint_A, Constraint_b, [], [], [], [], [], options);
if ~isempty(u) % get optimal input
acc_n = u(1);
beta_n = u(2);
input = [acc_n; beta_n];
e = 1;
if v >= target_speed + 0.5
acc_flag = 1;
end
else % no optimal input, the ego vehicle enter BL or BR state, drives back to its current lane
%% predictive calculation, to determine if the ego vehicle can change the lane through acceleration
if ~isempty(car_ft)
x_carft_rear = car_ft.state(1) - l_rc;
v_carft = car_ft.state(4);
tmp3 = -x_carft_rear + x + (v * (lim_speed - v) / self.goal.lim_acc + (lim_speed - v)^2 / 2 / self.goal.lim_acc) - l_fc - v_carft * (lim_speed - v) / self.goal.lim_acc - 0.1 * safety_factor * v_carft;
end
if ~isempty(car_fc)
x_carfc_rear = car_fc.state(1) - l_rc;
v_carfc = car_fc.state(4);
tmp1 = x_carfc_rear - x - (v * (lim_speed - v) / self.goal.lim_acc + (lim_speed - v)^2 / 2 / self.goal.lim_acc) - l_fc + v_carfc * (lim_speed - v) / self.goal.lim_acc - 0.1 * safety_factor * v;
end
if ~isempty(car_bt)
x_carbt_front = car_bt.state(1) + l_fc;
v_carbt = car_bt.state(4);
tmp2 = x - x_carbt_front - l_rc + (v * (lim_speed - v) / self.goal.lim_acc + (lim_speed - v)^2 / 2 / self.goal.lim_acc) - v_carbt * (lim_speed - v) / self.goal.lim_acc - 0.1 * safety_factor * v_carbt;
end
if (~isempty(car_ft) & ~isempty(car_fc) & (tmp3 >= 0 & tmp1 >= 0)) | (~isempty(car_ft) & isempty(car_fc) & (tmp3 >= 0))
track_speed = lim_speed;
acc_flag = 1;
elseif (~isempty(car_bt) & (~isempty(car_ft)) & (~isempty(car_fc)) & (tmp2 >= 0 & tmp1 >= 0 & tmp3 >= 0)) | (~isempty(car_bt) & (isempty(car_ft)) & (~isempty(car_fc)) & (tmp2 >= 0 & tmp1 >= 0)) | (~isempty(car_bt) & (~isempty(car_ft)) & (isempty(car_fc)) & (tmp2 >= 0 & tmp3 >= 0)) | (~isempty(car_bt) & (isempty(car_ft)) & (isempty(car_fc)) & (tmp2 >= 0))
track_speed = lim_speed;
acc_flag = 1;
else
track_speed = target_speed;
end
%% lateral position CLF
h_y = y - (current_lane_id - 0.5) * self.straightlane.lane_width;
V_y = h_y^2;
phi0_y = 2 * h_y * (v * sin(psi)) + alpha_y * V_y;
phi1_y = [0, 2 * h_y * v * cos(psi)];
%% velocity CLF
h_v = v - track_speed;
V_v = h_v^2;
phi0_v = alpha_v * V_v;
phi1_v = [2 * h_v * 1, 0];
%% yaw angle CLF
h_yaw = psi;
V_yaw = h_yaw^2;
phi0_yaw = alpha_yaw * V_yaw;
phi1_yaw = [0, 2 * h_yaw * v * l_r];
Aclf = [phi1_y, -1, 0, 0; ...
phi1_v, 0, -1, 0; ...
phi1_yaw, 0, 0, -1;];
bclf = [-phi0_y; -phi0_v; -phi0_yaw];
if lane_id == current_lane_id % the ego vehicle is already in its current lane,
% FSM enters ACC state, no car_ft and car_bt relevant CBF
Acbf3 = [0, 0, 0, 0, 0];
bcbf3 = [0];
Acbf4 = [0, 0, 0, 0, 0];
bcbf4 = [0];
Acbf5 = [0, 0, 0, 0, 0];
bcbf5 = [0];
Acbf6 = [0, 0, 0, 0, 0];
bcbf6 = [0];
end
Constraint_A = [Aclf; Acbf2; Acbf3; Acbf5; A_u; A_u0];
Constraint_b = [bclf; bcbf2; bcbf3; bcbf5; b_u; b_u0];
H = self.param_opt.H;
F = self.param_opt.F;
options = optimoptions('quadprog', 'Display', 'off');
u = quadprog(H, F, Constraint_A, Constraint_b, [], [], [], [], [], options);
if (~isempty(u))
acc_n = u(1);
beta_n = u(2);
input = [acc_n; beta_n];
e = 0;
else % the ego vehicle can not meet safety-critical requirement
error('fail')
end
end
end
function [acc, beta] = unpack_input(self, input)
acc = input(1);
beta = input(2);
end
function [x, y, psi, v] = unpack_state(self, state)
x = state(1);
y = state(2);
psi = state(3);
v = state(4);
end
end
end