matlab实现teb弹性时间带

### Matlab 中实现 TEB (Time-Elastic Band) 算法 TEB算法是一种用于路径规划的技术，特别适用于机器人导航中的轨迹优化。该方法通过弹性带模型来表示时间和空间上的路径，并对其进行优化以避开障碍物并平滑路径。 在Matlab中实现TEB算法涉及多个方面，包括定义环境、初始化参数以及编写核心计算逻辑。下面是一个简化版的TEB算法实现示例： ```matlab function teb_path = timeElasticBand(start, goal, obstacles) % TIMEELASTICBAND Implements Time Elastic Band algorithm. % % Inputs: % start - Starting point of the path as a vector [x y]. % goal - Goal position of the path as a vector [x y]. % obstacles- Matrix where each row represents an obstacle center and radius. %% Initialization num_points = 20; % Number of points on the initial straight line between start and end initial_path = linspace(start, goal, num_points); teb_path = initial_path; max_iterations = 100; tolerance = 0.01; lambda_att = 1.0; % Attractive force coefficient towards target mu_rep = 5.0; % Repulsive force coefficient from obstacles for iter = 1:max_iterations %% Compute Forces Acting On Each Point In The Path forces = zeros(size(teb_path)); % Add attractive force toward next waypoint for i = 1:(length(teb_path)-1) diff_to_next = teb_path(i+1,:) - teb_path(i,:); norm_diff = sqrt(sum(diff_to_next.^2)); if(norm_diff ~= 0) forces(i,:) = lambda_att * diff_to_next / norm_diff; end end % Add repulsive forces away from all obstacles for k = 1:size(obstacles, 1) obs_center = obstacles(k, 1:2)'; obs_radius = obstacles(k, 3); for j = 1:length(teb_path) dist_to_obs = sqrt(sum((obs_center - teb_path(j,:)).^2)); if(dist_to_obs < obs_radius + tolerance) direction_from_obs = (teb_path(j,:) - obs_center)/dist_to_obs; forces(j,:) = forces(j,:) + mu_rep*(1/dist_to_obs^2)*direction_from_obs; end end end %% Update Positions Based On Computed Forces step_size = 0.1; new_positions = teb_path + step_size*forces; %% Check Convergence And Termination Conditions movement_magnitude = mean(sqrt(sum(forces.^2, 2))); if(movement_magnitude < tolerance || iter >= max_iterations) break; else teb_path = new_positions; end end ``` 此代码片段展示了如何创建一个简单的TEB模拟，在给定起点和终点的情况下考虑静态圆形障碍物的影响。实际应用可能更加复杂，涉及到动态障碍检测和其他高级特性[^1]。