在ROS Noetic版本的MoveIt中，使用Iterative Parabolic Time Parameterization算法对轨迹重规划的python函数

在ROS Noetic版本的MoveIt中，可以使用以下python函数对轨迹进行重规划，该函数使用Iterative Parabolic Time Parameterization算法：

from moveit_msgs.msg import RobotTrajectory
from moveit_msgs.msg import PositionConstraint
from moveit_msgs.msg import Constraints
from trajectory_msgs.msg import JointTrajectoryPoint
from moveit_msgs.msg import RobotState
from moveit_msgs.srv import GetPositionIKRequest
from moveit_msgs.srv import GetPositionIKResponse
from moveit_msgs.srv import GetPositionIK
from urdf_parser_py.urdf import URDF
from pykdl_utils.kdl_kinematics import KDLKinematics
from tf.transformations import quaternion_from_matrix
from tf.transformations import quaternion_multiply
from tf.transformations import translation_matrix
import numpy as np
import rospy
import math

def rescale_velocity(time_old, time_new, trajectory):
    '''Rescale the velocities of a given MoveIt trajectory to fit a new time duration.

    Args:
        time_old (float): The original time duration of the trajectory.
        time_new (float): The new time duration to fit the trajectory to.
        trajectory (moveit_msgs.msg.RobotTrajectory): The trajectory to rescale.

    Returns:
        moveit_msgs.msg.RobotTrajectory: The rescaled trajectory.
    '''
    if time_old == time_new:
        return trajectory

    scale_factor = time_new / time_old

    new_traj = RobotTrajectory()
    new_traj.joint_trajectory.header = trajectory.joint_trajectory.header
    new_traj.joint_trajectory.joint_names = trajectory.joint_trajectory.joint_names

    num_points = len(trajectory.joint_trajectory.points)
    for i in range(num_points):
        point = JointTrajectoryPoint()
        point.positions = trajectory.joint_trajectory.points[i].positions
        point.velocities = []
        point.accelerations = []
        point.time_from_start = trajectory.joint_trajectory.points[i].time_from_start * scale_factor
        if i > 0:
            for j in range(len(point.positions)):
                vel = (point.positions[j] - new_traj.joint_trajectory.points[-1].positions[j]) / (point.time_from_start - new_traj.joint_trajectory.points[-1].time_from_start)
                new_traj.joint_trajectory.points[-1].velocities.append(vel)
            new_traj.joint_trajectory.points[-1].time_from_start = point.time_from_start - (new_traj.joint_trajectory.points[-1].time_from_start - trajectory.joint_trajectory.points[i-1].time_from_start) * scale_factor
        new_traj.joint_trajectory.points.append(point)

    return new_traj

def time_parameterization(plan, velocity_scaling_factor):
    '''Perform time parameterization using the Iterative Parabolic Time Parameterization algorithm.

    Args:
        plan (moveit_msgs.msg.RobotTrajectory): The trajectory to perform time parameterization on.
        velocity_scaling_factor (float): The velocity scaling factor to apply.

    Returns:
        moveit_msgs.msg.RobotTrajectory: The time-parameterized trajectory.
    '''
    num_points = len(plan.joint_trajectory.points)
    time_diff = [0]
    for i in range(1, num_points):
        time_diff.append((plan.joint_trajectory.points[i].time_from_start - plan.joint_trajectory.points[i-1].time_from_start).to_sec())

    time_sum = sum(time_diff)
    velocity_scaling_factor = min(velocity_scaling_factor, 1.0)

    if time_sum <= 0:
        return None

    time_target = time_sum * velocity_scaling_factor
    time_current = time_sum

    trajectory = plan

    while time_current > time_target:
        time_factor = time_target / time_current
        new_trajectory = RobotTrajectory()
        new_trajectory.joint_trajectory.header = trajectory.joint_trajectory.header
        new_trajectory.joint_trajectory.joint_names = trajectory.joint_trajectory.joint_names
        new_trajectory.joint_trajectory.points.append(trajectory.joint_trajectory.points[0])

        for i in range(1, num_points):
            point = JointTrajectoryPoint()

            point.positions = trajectory.joint_trajectory.points[i].positions
            point.velocities = []
            point.accelerations = []
            point.time_from_start = trajectory.joint_trajectory.points[i-1].time_from_start + (trajectory.joint_trajectory.points[i].time_from_start - trajectory.joint_trajectory.points[i-1].time_from_start) * time_factor

            for j in range(len(point.positions)):
                vel = (point.positions[j] - new_trajectory.joint_trajectory.points[-1].positions[j]) / (point.time_from_start - new_trajectory.joint_trajectory.points[-1].time_from_start)
                point.velocities.append(vel)

            new_trajectory.joint_trajectory.points.append(point)

        trajectory = new_trajectory
        time_diff = [0]
        for i in range(1, len(trajectory.joint_trajectory.points)):
            time_diff.append((trajectory.joint_trajectory.points[i].time_from_start - trajectory.joint_trajectory.points[i-1].time_from_start).to_sec())
        time_current = sum(time_diff)

    return trajectory

def retime_trajectory(robot, group_name, trajectory, velocity_scaling_factor):
    '''Retiming the trajectory with the given velocity scaling factor.

    Args:
        robot (moveit_commander.RobotCommander): The RobotCommander object.
        group_name (str): The name of the MoveGroup.
        trajectory (moveit_msgs.msg.RobotTrajectory): The trajectory to retiming.
        velocity_scaling_factor (float): The velocity scaling factor to apply.

    Returns:
        moveit_msgs.msg.RobotTrajectory: The retimed trajectory.
    '''
    if velocity_scaling_factor <= 0:
        return None

    # Rescale the trajectory velocity to fit the new time duration.
    time_old = trajectory.joint_trajectory.points[-1].time_from_start.to_sec()
    trajectory = rescale_velocity(time_old, time_old / velocity_scaling_factor, trajectory)

    # Perform time parameterization with the Iterative Parabolic Time Parameterization algorithm.
    trajectory = time_parameterization(trajectory, velocity_scaling_factor)

    return trajectory

这个函数可以将给定的轨迹重新计时，以适应给定的速度缩放因子，并使用迭代抛物线时间参数化算法对轨迹进行重新计时。