hexapod/software/rpi/path_generator.py

#!python
#
# 2021  Zhengyu Peng
# Website: https://zpeng.me
#
# `                      `
# -:.                  -#:
# -//:.              -###:
# -////:.          -#####:
# -/:.://:.      -###++##:
# ..   `://:-  -###+. :##:
#        `:/+####+.   :##:
# .::::::::/+###.     :##:
# .////-----+##:    `:###:
#  `-//:.   :##:  `:###/.
#    `-//:. :##:`:###/.
#      `-//:+######/.
#        `-/+####/.
#          `+##+.
#           :##:
#           :##:
#           :##:
#           :##:
#           :##:
#            .+:

from lib import semicircle_generator, semicircle2_generator
from lib import path_rotate_z
from lib import get_rotate_x_matrix, get_rotate_y_matrix, get_rotate_z_matrix
import numpy as np


def gen_forward_path(standby_coordinate,
                     g_steps=20,
                     g_radius=25):
    assert (g_steps % 4) == 0

    halfsteps = int(g_steps/2)

    path = np.zeros((g_steps, 6, 3))

    semi_circle = semicircle_generator(g_radius, g_steps)

    path[:, [0, 2, 4], :] = np.tile(semi_circle[:, np.newaxis, :], (1, 3, 1))
    path[:, [1, 3, 5], :] = np.tile(
        np.roll(semi_circle[:, np.newaxis, :], halfsteps, axis=0), (1, 3, 1))

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_backward_path(standby_coordinate,
                      g_steps=20,
                      g_radius=25):
    assert (g_steps % 4) == 0

    halfsteps = int(g_steps/2)

    path = np.zeros((g_steps, 6, 3))

    semi_circle = semicircle_generator(g_radius, g_steps, reverse=True)

    path[:, [0, 2, 4], :] = np.tile(semi_circle[:, np.newaxis, :], (1, 3, 1))
    path[:, [1, 3, 5], :] = np.tile(
        np.roll(semi_circle[:, np.newaxis, :], halfsteps, axis=0), (1, 3, 1))

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_fastforward_path(standby_coordinate,
                         g_steps=20,
                         y_radius=50,
                         z_radius=30,
                         x_radius=10):
    assert (g_steps % 2) == 0

    halfsteps = int(g_steps/2)

    path = np.zeros((g_steps, 6, 3))
    semi_circle_r = semicircle2_generator(
        g_steps, y_radius, z_radius, x_radius)
    semi_circle_l = semicircle2_generator(
        g_steps, y_radius, z_radius, -x_radius)

    path[:, [0, 2], :] = np.tile(semi_circle_r[:, np.newaxis, :], (1, 2, 1))
    path[:, 1, :] = np.roll(semi_circle_r, halfsteps, axis=0)
    path[:, 4, :] = semi_circle_l
    path[:, [3, 5], :] = np.tile(
        np.roll(semi_circle_l[:, np.newaxis, :], halfsteps, axis=0), (1, 2, 1))

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_fastbackward_path(standby_coordinate,
                          g_steps=20,
                          y_radius=50,
                          z_radius=30,
                          x_radius=10):
    assert (g_steps % 2) == 0

    halfsteps = int(g_steps/2)

    path = np.zeros((g_steps, 6, 3))
    semi_circle_r = semicircle2_generator(
        g_steps, y_radius, z_radius, x_radius, reverse=True)
    semi_circle_l = semicircle2_generator(
        g_steps, y_radius, z_radius, -x_radius, reverse=True)

    path[:, [0, 2], :] = np.tile(semi_circle_r[:, np.newaxis, :], (1, 2, 1))
    path[:, 1, :] = np.roll(semi_circle_r, halfsteps, axis=0)
    path[:, 4, :] = semi_circle_l
    path[:, [3, 5], :] = np.tile(
        np.roll(semi_circle_l[:, np.newaxis, :], halfsteps, axis=0), (1, 2, 1))

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_leftturn_path(standby_coordinate,
                      g_steps=20,
                      g_radius=25):
    assert (g_steps % 4) == 0
    halfsteps = int(g_steps/2)

    path = np.zeros((g_steps, 6, 3))

    semi_circle = semicircle_generator(g_radius, g_steps)
    mir_path = np.roll(semi_circle, halfsteps, axis=0)

    path[:, 0, :] = path_rotate_z(semi_circle, 45)
    path[:, 1, :] = path_rotate_z(mir_path, 0)
    path[:, 2, :] = path_rotate_z(semi_circle, 315)
    path[:, 3, :] = path_rotate_z(mir_path, 225)
    path[:, 4, :] = path_rotate_z(semi_circle, 180)
    path[:, 5, :] = path_rotate_z(mir_path, 135)

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_rightturn_path(standby_coordinate,
                       g_steps=20,
                       g_radius=25):
    assert (g_steps % 4) == 0
    halfsteps = int(g_steps/2)

    semi_circle = semicircle_generator(g_radius, g_steps)
    mir_path = np.roll(semi_circle, halfsteps, axis=0)

    path = np.zeros((g_steps, 6, 3))
    path[:, 0, :] = path_rotate_z(semi_circle, 45+180)
    path[:, 1, :] = path_rotate_z(mir_path, 0+180)
    path[:, 2, :] = path_rotate_z(semi_circle, 315+180)
    path[:, 3, :] = path_rotate_z(mir_path, 225+180)
    path[:, 4, :] = path_rotate_z(semi_circle, 180+180)
    path[:, 5, :] = path_rotate_z(mir_path, 135+180)

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_shiftleft_path(standby_coordinate,
                       g_steps=20,
                       g_radius=25):
    assert (g_steps % 4) == 0
    halfsteps = int(g_steps/2)

    semi_circle = semicircle_generator(g_radius, g_steps)
    # shift 90 degree to make the path "left" shift
    semi_circle = np.array(path_rotate_z(semi_circle, 90))
    mir_path = np.roll(semi_circle, halfsteps, axis=0)

    path = np.zeros((g_steps, 6, 3))
    path[:, [0, 2, 4], :] = np.tile(semi_circle[:, np.newaxis, :], (1, 3, 1))
    path[:, [1, 3, 5], :] = np.tile(mir_path[:, np.newaxis, :], (1, 3, 1))

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_shiftright_path(standby_coordinate,
                        g_steps=20,
                        g_radius=25):
    assert (g_steps % 4) == 0
    halfsteps = int(g_steps/2)

    semi_circle = semicircle_generator(g_radius, g_steps)
    # shift 90 degree to make the path "left" shift
    semi_circle = np.array(path_rotate_z(semi_circle, 270))
    mir_path = np.roll(semi_circle, halfsteps, axis=0)

    path = np.zeros((g_steps, 6, 3))
    path[:, [0, 2, 4], :] = np.tile(semi_circle[:, np.newaxis, :], (1, 3, 1))
    path[:, [1, 3, 5], :] = np.tile(mir_path[:, np.newaxis, :], (1, 3, 1))

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_climb_path(standby_coordinate,
                   g_steps=20,
                   y_radius=20,
                   z_radius=80,
                   x_radius=30,
                   z_shift=-30):
    assert (g_steps % 4) == 0
    halfsteps = int(g_steps/2)

    rpath = semicircle2_generator(g_steps, y_radius, z_radius, x_radius)
    rpath[:, 2] = rpath[:, 2]+z_shift

    lpath = semicircle2_generator(g_steps, y_radius, z_radius, -x_radius)
    lpath[:, 2] = lpath[:, 2]+z_shift

    mir_rpath = np.roll(rpath, halfsteps, axis=0)
    mir_lpath = np.roll(lpath, halfsteps, axis=0)

    path = np.zeros((g_steps, 6, 3))
    path[:, 0, :] = rpath
    path[:, 1, :] = mir_rpath
    path[:, 2, :] = rpath
    path[:, 3, :] = mir_lpath
    path[:, 4, :] = lpath
    path[:, 5, :] = mir_lpath

    return path+np.tile(standby_coordinate, (g_steps, 1, 1))


def gen_rotatex_path(standby_coordinate,
                     g_steps=20,
                     swing_angle=15,
                     y_radius=15):
    assert (g_steps % 4) == 0
    quarter = int(g_steps/4)

    path = np.zeros((g_steps, 6, 3))

    step_angle = swing_angle / quarter
    step_offset = y_radius / quarter

    scx = np.append(standby_coordinate, np.ones((6, 1)), axis=1)

    for i in range(quarter):
        m = get_rotate_x_matrix(swing_angle - i*step_angle)
        m[1, 3] = -i * step_offset

        path[i, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    for i in range(quarter):
        m = get_rotate_x_matrix(-i*step_angle)
        m[1, 3] = -y_radius + i * step_offset

        path[i+quarter, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    for i in range(quarter):
        m = get_rotate_x_matrix(i*step_angle-swing_angle)
        m[1, 3] = i * step_offset

        path[i+quarter*2, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    for i in range(quarter):
        m = get_rotate_x_matrix(i*step_angle)
        m[1, 3] = y_radius-i * step_offset

        path[i+quarter*3, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    return path


def gen_rotatey_path(standby_coordinate,
                     g_steps=20,
                     swing_angle=15,
                     x_radius=15):
    assert (g_steps % 4) == 0
    quarter = int(g_steps/4)

    path = np.zeros((g_steps, 6, 3))

    step_angle = swing_angle / quarter
    step_offset = x_radius / quarter

    scx = np.append(standby_coordinate, np.ones((6, 1)), axis=1)

    for i in range(quarter):
        m = get_rotate_y_matrix(swing_angle - i*step_angle)
        m[1, 3] = -i * step_offset

        path[i, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    for i in range(quarter):
        m = get_rotate_y_matrix(-i*step_angle)
        m[1, 3] = -x_radius + i * step_offset

        path[i+quarter, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    for i in range(quarter):
        m = get_rotate_y_matrix(i*step_angle-swing_angle)
        m[1, 3] = i * step_offset

        path[i+quarter*2, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    for i in range(quarter):
        m = get_rotate_y_matrix(i*step_angle)
        m[1, 3] = x_radius-i * step_offset

        path[i+quarter*3, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    return path


def gen_rotatez_path(standby_coordinate,
                     g_steps=20,
                     z_lift=4.5,
                     xy_radius=1):
    assert (g_steps % 4) == 0

    path = np.zeros((g_steps, 6, 3))

    step_angle = 2*np.pi / g_steps
    scx = np.append(standby_coordinate, np.ones((6, 1)), axis=1)

    for i in range(g_steps):
        x = xy_radius * np.cos(i*step_angle)
        y = xy_radius * np.sin(i*step_angle)

        m = get_rotate_y_matrix(np.arctan2(
            x, z_lift)*180/np.pi) * get_rotate_x_matrix(np.arctan2(y, z_lift)*180/np.pi)

        path[i, :, :] = ((np.matmul(m, scx.T)).T)[:, :-1]

    return path


def gen_twist_path(standby_coordinate,
                   g_steps=20,
                   raise_angle=3,
                   twist_x_angle=20,
                   twise_y_angle=12):
    assert (g_steps % 4) == 0

    quarter = int(g_steps / 4)
    step_x_angle = twist_x_angle / quarter
    step_y_angle = twise_y_angle / quarter
    scx = np.append(standby_coordinate, np.ones((6, 1)), axis=1)

    m = get_rotate_x_matrix(raise_angle)

    path = np.zeros((g_steps, 6, 3))

    for i in range(quarter):
        temp = m * get_rotate_z_matrix(i*step_x_angle) * \
            get_rotate_x_matrix(i*step_y_angle)

        path[i, :, :] = ((np.matmul(temp, scx.T)).T)[:, :-1]

    for i in range(quarter):
        temp = m * get_rotate_z_matrix((quarter-i)*step_x_angle) * \
            get_rotate_x_matrix((quarter-i)*step_y_angle)

        path[i+quarter*1, :, :] = ((np.matmul(temp, scx.T)).T)[:, :-1]

    for i in range(quarter):
        temp = m * get_rotate_z_matrix(-i*step_x_angle) * \
            get_rotate_x_matrix(i*step_y_angle)

        path[i+quarter*2, :, :] = ((np.matmul(temp, scx.T)).T)[:, :-1]

    for i in range(quarter):
        temp = m * get_rotate_z_matrix((-quarter+i)*step_x_angle) * \
            get_rotate_x_matrix((quarter-i)*step_y_angle)

        path[i+quarter*3, :, :] = ((np.matmul(temp, scx.T)).T)[:, :-1]

    return path