import numpy as np from scipy.interpolate import interp1d def compute_path_from_wp(start_xp, start_yp, step=0.1): """ params: start_xp (array-like): 1D array of x-positions start_yp (array-like): 1D array of y-positions step (float): interpolation step size output: ndarray of shape (3,N) representing the path as x,y,heading """ final_xp = [] final_yp = [] delta = step # [m] for idx in range(len(start_xp) - 1): # find the distance between consecutive waypoints section_len = np.sum( np.sqrt( np.power(np.diff(start_xp[idx : idx + 2]), 2) + np.power(np.diff(start_yp[idx : idx + 2]), 2) ) ) # how many interpolated points are needed to reach the next waypoint interp_range = np.linspace(0, 1, np.floor(section_len / delta).astype(int)) # interpolate between waypoints fx = interp1d(np.linspace(0, 1, 2), start_xp[idx : idx + 2], kind=1) fy = interp1d(np.linspace(0, 1, 2), start_yp[idx : idx + 2], kind=1) # append the interpolated points to the final path final_xp = np.append(final_xp, fx(interp_range)[1:]) final_yp = np.append(final_yp, fy(interp_range)[1:]) dx = np.append(0, np.diff(final_xp)) dy = np.append(0, np.diff(final_yp)) theta = np.arctan2(dy, dx) return np.vstack((final_xp, final_yp, theta)) def get_nn_idx(state, path): """ Helper function to find the index of the nearest path point to the current state. Args: state (array-like): Current state [x, y, theta] path (ndarray): Path points Returns: int: Index of the nearest path point """ # distances = np.hypot(path[0, :] - state[0], path[1, :] - state[1]) distances = np.linalg.norm(path[:2]-state[:2].reshape(2,1), axis=0) return np.argmin(distances) def fix_angle_reference(angle_ref, angle_init): """ Removes jumps greater than 2PI to smooth the heading. Args: angle_ref (array-like): Reference angles angle_init (float): Initial angle Returns: array-like: Smoothed reference angles """ diff_angle = angle_ref - angle_init diff_angle = np.unwrap(diff_angle) return angle_init + diff_angle def get_ref_trajectory(state, path, target_v, T, DT): """ Generates a reference trajectory for the Roomba. Args: state (array-like): Current state [x, y, theta] path (ndarray): Path points [x, y, theta] in the global frame target_v (float): Desired speed T (float): Control horizon duration DT (float): Control horizon time-step Returns: ndarray: Reference trajectory [x_k, y_k, theta_k] in the ego frame """ K = int(T / DT) xref = np.zeros((3, K)) # Reference trajectory for [x, y, theta] # find the nearest path point to the current state ind = get_nn_idx(state, path) # calculate the cumulative distance along the path cdist = np.append([0.0], np.cumsum(np.hypot(np.diff(path[0, :]), np.diff(path[1, :])))) cdist = np.clip(cdist, cdist[0], cdist[-1]) # determine where we want the robot to be at each time step start_dist = cdist[ind] interp_points = [d * DT * target_v + start_dist for d in range(1, K + 1)] # interpolate between these points to get the reference trajectory xref[0, :] = np.interp(interp_points, cdist, path[0, :]) xref[1, :] = np.interp(interp_points, cdist, path[1, :]) xref[2, :] = np.interp(interp_points, cdist, path[2, :]) # Transform to ego frame dx = xref[0, :] - state[0] dy = xref[1, :] - state[1] xref[0, :] = dx * np.cos(-state[2]) - dy * np.sin(-state[2]) # X xref[1, :] = dy * np.cos(-state[2]) + dx * np.sin(-state[2]) # Y xref[2, :] = path[2, ind] - state[2] # Theta # Normalize the angles xref[2, :] = (xref[2, :] + np.pi) % (2.0 * np.pi) - np.pi xref[2, :] = fix_angle_reference(xref[2, :], xref[2, 0]) return xref