悉尼大学停车场SLAM matlab

%------------------------------------------------------------------------- % FILE: slam.m % DESC: Implements the SLAM algorithm based on a robot model and sensor % data from Nebot. %landmarks(真实路标) %estbeac=estimation(估计)+beacon(路标)，将estbeac的值赋给landmarks然后将estbeac清除。 %xest 状态矩阵 %Pest 协方差矩阵 %A W Jh 雅可比矩阵 %Q 过程激励噪声协方差矩阵 %k 迭代次数 %K 卡尔曼增益 %numStates 状态的数量 初始化时候就三个，即位置(x，y)和姿态(phi) %phi 姿态，即与x轴的夹角 %Steering 转向角 %alpha 转向角 %Ve = Velocity 后轮的转速 %Vc 车水平平移速度 %zlaser=[rangeArray; bearingArray]; 机器人与路标的距离和方位 %-------------------------------------------------------------------------- clear all; clc; load('data_set'); load('beac_juan3.mat'); %beac_juan3.mat中内容为路标,命令whos –file查看该文件中的内容 landmarks=estbeac; clear estbeac; % true landmark positions (measured w/GPS sensor) %--------------------- DATA INITIALIZATION ----------------------------- % Vehicle constants L=2.83; % distance between front and rear axles(前后轮轴之间的距离) h=0.76; % distance between center of rear axle and encoder(后轮轴中心与编码器的距离) b=0.5; % vertical distance from rear axle to laser(后轮轴中心到激光传感器的垂直距离) a=3.78; % horizontal distance from rear axle to laser(后轮轴中心到激光传感器的水平距离) % EKF components used in multiple functions global xest Pest A Q W %定义全局变量 global numStates k xest = zeros(3,1); % state matrix Pest = zeros(3,3); % covariance matrix2 numStates=3; % initially, there are no landmarks(i.e. the number of value in the state matrix) % matrixes initialization A = zeros(3,3); % process model jacobian W = eye(3); % process noise jacobian Q = [.49 0 0; 0 .49 0; 0 0 (7*pi/180)^2]; Jh = zeros(2,3); % sensor model jacobian K = zeros(3,3); % kalman gain % initialize time To = min([TimeGPS(1),Time_VS(1),TimeLaser(1)]); % data starts being collected at 45 secs for some reason?? Time = Time - To; t=Time(1); tfinal = 112; % there is 112 seconds worth of data k=1; % loop iteration counter(循环迭代计数) % initialize estimates xest(1,1) = GPSLon(1); % x position of vehicle xest(2,1) = GPSLat(1); % y position of vehicle xest(3,1) = -126*pi/180; % phi of vehicle % LB(?):how to get this value? Pest(:,:) = [0.1, 0, 0; 0, 0.1, 0; 0, 0, 15*pi/180]; % initial inputs alpha = Steering(1); % measured steering angle(测量转向角) Ve = Velocity(1); % measured velocity at back wheel(测量后轮速率) Vc = Velocity(1) / (1 - (h/L)*tan(alpha)); % measured velocity transformed to vehicle center %--------------------- end of DATA INITIALIZATION ------------------------ disp('Running through Kalman filter...'); n_dsp = 0; %------------------ EXTENDED KALMAN FILTER PROCEDURE -------------------- while t<tfinal k=k+1; t=Time(k); dt=t-Time(k-1); % Calculate time update matrices (prediction step of kalman filter) % Vc and alpha are updated after prediction...therefore, Vc is Vc(k-1) & alpha is alpha(k-1) %下面是公式（1） phi = xest(3,k-1); % so I don't have to type in xest(3,k-1) for every phi below xest(1,k) = xest(1,k-1) + dt*Vc*cos(phi) - dt*Vc/L*tan(alpha)*(a*sin(phi)+b*cos(phi)); % x prediction xest(2,k) = xest(2,k-1) + dt*Vc*sin(phi) + dt*Vc/L*tan(alpha)*(a*cos(phi)-b*sin(phi)); % y prediction xest(3,k) = xest(3,k-1) + dt*Vc/L*tan(alpha); % phi prediction xest(3,k) = normalizeAngle(xest(3,k)); % keep phi between -180 and 180 degrees % landmarks are assumed to be static, i.e. pi(k) = pi(k-1) if(numStates>3) for i=4:numStates xest(i,k)= xest(i,k-1); end end % Calculate Jacobian A based on vehicle model (df/dx) A(1,1)=1; A(1,2)=0; A(1,3) = -dt*Vc*sin(phi) - dt*Vc/L*tan(alpha)*(a*cos(phi)-b*sin(phi)); A(2,1)=0; A(2,2)=1; A(2,3) = dt*Vc*cos(phi) - dt*Vc/L*tan(alpha)*(a*sin(phi)+b*cos(phi)); A(3,1)=0; A(3,2)=0; A(3,3)=1; % rest of A (which is just 2 null matrices and 1 identity) is added in new_state function % Calculate prediction for covariance matrix Pest = A*Pest*A' + W*Q*W'; %(公式2) % Check to see if new velocity and steering measurements are available if Sensor(k)==2 % encoders(编码器) are sensor #2 Ve = Velocity(Index(k)); alpha = Steering(Index(k)); Vc = Ve / (1-(h/L)*tan(alpha)); end % Check to see if new laser(激光) data is available if (Sensor(k)==3 && t>1) % SICK is sensor #3 % from a single 180 degree scan, determine # of landmarks & center of each landmark [rangeArray bearingArray] = getLandmarkCenter(Laser(Index(k),:), Intensity(Index(k),:)); zlaser=[rangeArray; bearingArray]; % range/bearing data in observation model format numLandmarks = size(rangeArray,2); % number of LMs captured in a single scan for i=1:numLandmarks % for i = 1 to # of landmakrs picked up in single scan if(numStates==3) % if 1st observed landmark, update state and covariance new_state(zlaser(:,i)); % add new state (i.e. increase all matrix sizes) numStates = numStates + 2; % increase number of states by 2 (1 for xi, 1 for yi) [xest,Pest] = updateNew(zlaser(:,i)); % update state and covariance else % not 1st landmark -> check to make sure no LMs in range [dist,index]=nearby_LMs(zlaser(:,i)); % dist from observation to already incorporated LMs (< 3m) min_dist = 2; % minimum distance between landmark and observation if dist>min_dist % if dist to nearby_LM is > "min_dist", add observation as new LM new_state(zlaser(:,i)); % add new state (i.e. increase all matrix sizes) numStates = numStates + 2; % increase number of states by 2 (1 for xi, 1 for yi) [xest,Pest] = updateNew(zlaser(:,i)); % update state and covariance else % else find closest LM and associate closest = 4 + 2*(index-1); % find LM which is closest to observation [xest,Pest] = updateExisting(zlaser(:,i),closest); % update state and covariance end end end end % LB_add: display information if( floor(t/tfinal*100) > n_dsp) clc; n_dsp = floor(t/tfinal*100); str = sprintf('运行卡尔曼滤波... [%d%c]', n_dsp,'%'); disp(str); end end % end while %-------------- end of EXTENDED KALMAN FILTER PROCEDURE ----------------- %--------------------------- PLOT RESULTS -------------------------------- figure(1); hold on; plot(GPSLon(1:560),GPSLat(1:560)); % robot position (true) plot(xest(1,1:k),xest(2,1:k),'g'); % robot position (model) plot(landmarks(:,1),landmarks(:,2),'*'); % landmark position (true) for i=4:2:numStates plot(xest(i,k),xest(i+1,k),'r*'); % landmark position (