From 0edcd611095a8d9e6b200a53138566e5e824de2c Mon Sep 17 00:00:00 2001
From: Zhengyu Peng <rookie.dev@gmail.com>
Date: Fri, 10 Dec 2021 15:03:00 -0500
Subject: [PATCH] twist

---
 software/rpi/hexapod.py        |   4 +-
 software/rpi/path_generator.py | 212 ++++++++++++++++++++++++++++++++-
 2 files changed, 212 insertions(+), 4 deletions(-)

diff --git a/software/rpi/hexapod.py b/software/rpi/hexapod.py
index 7d6e03d..aca37ec 100644
--- a/software/rpi/hexapod.py
+++ b/software/rpi/hexapod.py
@@ -17,6 +17,7 @@ from path_generator import gen_leftturn_path, gen_rightturn_path
 from path_generator import gen_shiftleft_path, gen_shiftright_path
 from path_generator import gen_climb_path
 from path_generator import gen_rotatex_path, gen_rotatey_path, gen_rotatez_path
+from path_generator import gen_twist_path
 
 
 SIN30 = 0.5
@@ -105,6 +106,7 @@ class Hexapod:
         self.rotatex_path = gen_rotatex_path(self.standby_coordinate)
         self.rotatey_path = gen_rotatey_path(self.standby_coordinate)
         self.rotatez_path = gen_rotatez_path(self.standby_coordinate)
+        self.twist_path = gen_twist_path(self.standby_coordinate)
 
         self.standby()
         time.sleep(1)
@@ -138,7 +140,7 @@ class Hexapod:
 
         # self.move(self.rotatex_path, 0.005)
         for mm in range(0, 20):
-            self.move(self.rotatez_path, 0.005)
+            self.move(self.twist_path, 0.005)
 
         time.sleep(1)
         self.standby()
diff --git a/software/rpi/path_generator.py b/software/rpi/path_generator.py
index b2b89c0..ba63746 100644
--- a/software/rpi/path_generator.py
+++ b/software/rpi/path_generator.py
@@ -1,6 +1,6 @@
 from lib import semicircle_generator, semicircle2_generator
 from lib import path_rotate_z
-from lib import get_rotate_x_matrix, get_rotate_y_matrix
+from lib import get_rotate_x_matrix, get_rotate_y_matrix, get_rotate_z_matrix
 import numpy as np
 from collections import deque
 
@@ -424,6 +424,7 @@ def gen_rotatex_path(standby_coordinate):
     return path
     # return result, "matrix", 50, (0, quarter*2)
 
+
 def gen_rotatey_path(standby_coordinate):
     # standby_coordinate = np.ones((6,3))
     g_steps = 20
@@ -634,6 +635,7 @@ def gen_rotatey_path(standby_coordinate):
 
     return path
 
+
 def gen_rotatez_path(standby_coordinate):
     # standby_coordinate = np.ones((6,3))
     g_steps = 20
@@ -651,7 +653,8 @@ def gen_rotatez_path(standby_coordinate):
         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)
+        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, 0, 0] = standby_coordinate[0, 0]*m[0, 0]+standby_coordinate[0,
                                                                             1]*m[0, 1]+standby_coordinate[0, 2]*m[0, 2]+m[0, 3]
         path[i, 0, 1] = standby_coordinate[0, 0]*m[1, 0]+standby_coordinate[0,
@@ -694,5 +697,208 @@ def gen_rotatez_path(standby_coordinate):
         path[i, 5, 2] = standby_coordinate[5, 0]*m[2, 0]+standby_coordinate[5,
                                                                             1]*m[2, 1]+standby_coordinate[5, 2]*m[2, 2]+m[2, 3]
 
+    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
+
+    m = get_rotate_x_matrix(raise_angle)
+
+    path = np.zeros((g_steps, 6, 3))
 
-    return path
\ No newline at end of file
+    for i in range(quarter):
+        temp = m * get_rotate_z_matrix(i*step_x_angle) * \
+            get_rotate_x_matrix(i*step_y_angle)
+
+        idx = i+quarter*0
+
+        path[idx, 0, 0] = standby_coordinate[0, 0]*temp[0, 0]+standby_coordinate[0,
+                                                                                 1]*temp[0, 1]+standby_coordinate[0, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 0, 1] = standby_coordinate[0, 0]*temp[1, 0]+standby_coordinate[0,
+                                                                                 1]*temp[1, 1]+standby_coordinate[0, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 0, 2] = standby_coordinate[0, 0]*temp[2, 0]+standby_coordinate[0,
+                                                                                 1]*temp[2, 1]+standby_coordinate[0, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 1, 0] = standby_coordinate[1, 0]*temp[0, 0]+standby_coordinate[1,
+                                                                                 1]*temp[0, 1]+standby_coordinate[1, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 1, 1] = standby_coordinate[1, 0]*temp[1, 0]+standby_coordinate[1,
+                                                                                 1]*temp[1, 1]+standby_coordinate[1, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 1, 2] = standby_coordinate[1, 0]*temp[2, 0]+standby_coordinate[1,
+                                                                                 1]*temp[2, 1]+standby_coordinate[1, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 2, 0] = standby_coordinate[2, 0]*temp[0, 0]+standby_coordinate[2,
+                                                                                 1]*temp[0, 1]+standby_coordinate[2, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 2, 1] = standby_coordinate[2, 0]*temp[1, 0]+standby_coordinate[2,
+                                                                                 1]*temp[1, 1]+standby_coordinate[2, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 2, 2] = standby_coordinate[2, 0]*temp[2, 0]+standby_coordinate[2,
+                                                                                 1]*temp[2, 1]+standby_coordinate[2, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 3, 0] = standby_coordinate[3, 0]*temp[0, 0]+standby_coordinate[3,
+                                                                                 1]*temp[0, 1]+standby_coordinate[3, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 3, 1] = standby_coordinate[3, 0]*temp[1, 0]+standby_coordinate[3,
+                                                                                 1]*temp[1, 1]+standby_coordinate[3, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 3, 2] = standby_coordinate[3, 0]*temp[2, 0]+standby_coordinate[3,
+                                                                                 1]*temp[2, 1]+standby_coordinate[3, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 4, 0] = standby_coordinate[4, 0]*temp[0, 0]+standby_coordinate[4,
+                                                                                 1]*temp[0, 1]+standby_coordinate[4, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 4, 1] = standby_coordinate[4, 0]*temp[1, 0]+standby_coordinate[4,
+                                                                                 1]*temp[1, 1]+standby_coordinate[4, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 4, 2] = standby_coordinate[4, 0]*temp[2, 0]+standby_coordinate[4,
+                                                                                 1]*temp[2, 1]+standby_coordinate[4, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 5, 0] = standby_coordinate[5, 0]*temp[0, 0]+standby_coordinate[5,
+                                                                                 1]*temp[0, 1]+standby_coordinate[5, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 5, 1] = standby_coordinate[5, 0]*temp[1, 0]+standby_coordinate[5,
+                                                                                 1]*temp[1, 1]+standby_coordinate[5, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 5, 2] = standby_coordinate[5, 0]*temp[2, 0]+standby_coordinate[5,
+                                                                                 1]*temp[2, 1]+standby_coordinate[5, 2]*temp[2, 2]+temp[2, 3]
+    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)
+        idx = i+quarter*1
+
+        path[idx, 0, 0] = standby_coordinate[0, 0]*temp[0, 0]+standby_coordinate[0,
+                                                                                 1]*temp[0, 1]+standby_coordinate[0, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 0, 1] = standby_coordinate[0, 0]*temp[1, 0]+standby_coordinate[0,
+                                                                                 1]*temp[1, 1]+standby_coordinate[0, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 0, 2] = standby_coordinate[0, 0]*temp[2, 0]+standby_coordinate[0,
+                                                                                 1]*temp[2, 1]+standby_coordinate[0, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 1, 0] = standby_coordinate[1, 0]*temp[0, 0]+standby_coordinate[1,
+                                                                                 1]*temp[0, 1]+standby_coordinate[1, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 1, 1] = standby_coordinate[1, 0]*temp[1, 0]+standby_coordinate[1,
+                                                                                 1]*temp[1, 1]+standby_coordinate[1, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 1, 2] = standby_coordinate[1, 0]*temp[2, 0]+standby_coordinate[1,
+                                                                                 1]*temp[2, 1]+standby_coordinate[1, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 2, 0] = standby_coordinate[2, 0]*temp[0, 0]+standby_coordinate[2,
+                                                                                 1]*temp[0, 1]+standby_coordinate[2, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 2, 1] = standby_coordinate[2, 0]*temp[1, 0]+standby_coordinate[2,
+                                                                                 1]*temp[1, 1]+standby_coordinate[2, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 2, 2] = standby_coordinate[2, 0]*temp[2, 0]+standby_coordinate[2,
+                                                                                 1]*temp[2, 1]+standby_coordinate[2, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 3, 0] = standby_coordinate[3, 0]*temp[0, 0]+standby_coordinate[3,
+                                                                                 1]*temp[0, 1]+standby_coordinate[3, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 3, 1] = standby_coordinate[3, 0]*temp[1, 0]+standby_coordinate[3,
+                                                                                 1]*temp[1, 1]+standby_coordinate[3, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 3, 2] = standby_coordinate[3, 0]*temp[2, 0]+standby_coordinate[3,
+                                                                                 1]*temp[2, 1]+standby_coordinate[3, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 4, 0] = standby_coordinate[4, 0]*temp[0, 0]+standby_coordinate[4,
+                                                                                 1]*temp[0, 1]+standby_coordinate[4, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 4, 1] = standby_coordinate[4, 0]*temp[1, 0]+standby_coordinate[4,
+                                                                                 1]*temp[1, 1]+standby_coordinate[4, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 4, 2] = standby_coordinate[4, 0]*temp[2, 0]+standby_coordinate[4,
+                                                                                 1]*temp[2, 1]+standby_coordinate[4, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 5, 0] = standby_coordinate[5, 0]*temp[0, 0]+standby_coordinate[5,
+                                                                                 1]*temp[0, 1]+standby_coordinate[5, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 5, 1] = standby_coordinate[5, 0]*temp[1, 0]+standby_coordinate[5,
+                                                                                 1]*temp[1, 1]+standby_coordinate[5, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 5, 2] = standby_coordinate[5, 0]*temp[2, 0]+standby_coordinate[5,
+                                                                                 1]*temp[2, 1]+standby_coordinate[5, 2]*temp[2, 2]+temp[2, 3]
+    for i in range(quarter):
+        temp = m * get_rotate_z_matrix(-i*step_x_angle) * \
+            get_rotate_x_matrix(i*step_y_angle)
+        idx = i+quarter*2
+
+        path[idx, 0, 0] = standby_coordinate[0, 0]*temp[0, 0]+standby_coordinate[0,
+                                                                                 1]*temp[0, 1]+standby_coordinate[0, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 0, 1] = standby_coordinate[0, 0]*temp[1, 0]+standby_coordinate[0,
+                                                                                 1]*temp[1, 1]+standby_coordinate[0, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 0, 2] = standby_coordinate[0, 0]*temp[2, 0]+standby_coordinate[0,
+                                                                                 1]*temp[2, 1]+standby_coordinate[0, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 1, 0] = standby_coordinate[1, 0]*temp[0, 0]+standby_coordinate[1,
+                                                                                 1]*temp[0, 1]+standby_coordinate[1, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 1, 1] = standby_coordinate[1, 0]*temp[1, 0]+standby_coordinate[1,
+                                                                                 1]*temp[1, 1]+standby_coordinate[1, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 1, 2] = standby_coordinate[1, 0]*temp[2, 0]+standby_coordinate[1,
+                                                                                 1]*temp[2, 1]+standby_coordinate[1, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 2, 0] = standby_coordinate[2, 0]*temp[0, 0]+standby_coordinate[2,
+                                                                                 1]*temp[0, 1]+standby_coordinate[2, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 2, 1] = standby_coordinate[2, 0]*temp[1, 0]+standby_coordinate[2,
+                                                                                 1]*temp[1, 1]+standby_coordinate[2, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 2, 2] = standby_coordinate[2, 0]*temp[2, 0]+standby_coordinate[2,
+                                                                                 1]*temp[2, 1]+standby_coordinate[2, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 3, 0] = standby_coordinate[3, 0]*temp[0, 0]+standby_coordinate[3,
+                                                                                 1]*temp[0, 1]+standby_coordinate[3, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 3, 1] = standby_coordinate[3, 0]*temp[1, 0]+standby_coordinate[3,
+                                                                                 1]*temp[1, 1]+standby_coordinate[3, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 3, 2] = standby_coordinate[3, 0]*temp[2, 0]+standby_coordinate[3,
+                                                                                 1]*temp[2, 1]+standby_coordinate[3, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 4, 0] = standby_coordinate[4, 0]*temp[0, 0]+standby_coordinate[4,
+                                                                                 1]*temp[0, 1]+standby_coordinate[4, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 4, 1] = standby_coordinate[4, 0]*temp[1, 0]+standby_coordinate[4,
+                                                                                 1]*temp[1, 1]+standby_coordinate[4, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 4, 2] = standby_coordinate[4, 0]*temp[2, 0]+standby_coordinate[4,
+                                                                                 1]*temp[2, 1]+standby_coordinate[4, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 5, 0] = standby_coordinate[5, 0]*temp[0, 0]+standby_coordinate[5,
+                                                                                 1]*temp[0, 1]+standby_coordinate[5, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 5, 1] = standby_coordinate[5, 0]*temp[1, 0]+standby_coordinate[5,
+                                                                                 1]*temp[1, 1]+standby_coordinate[5, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 5, 2] = standby_coordinate[5, 0]*temp[2, 0]+standby_coordinate[5,
+                                                                                 1]*temp[2, 1]+standby_coordinate[5, 2]*temp[2, 2]+temp[2, 3]
+    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)
+        idx = i+quarter*3
+
+        path[idx, 0, 0] = standby_coordinate[0, 0]*temp[0, 0]+standby_coordinate[0,
+                                                                                 1]*temp[0, 1]+standby_coordinate[0, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 0, 1] = standby_coordinate[0, 0]*temp[1, 0]+standby_coordinate[0,
+                                                                                 1]*temp[1, 1]+standby_coordinate[0, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 0, 2] = standby_coordinate[0, 0]*temp[2, 0]+standby_coordinate[0,
+                                                                                 1]*temp[2, 1]+standby_coordinate[0, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 1, 0] = standby_coordinate[1, 0]*temp[0, 0]+standby_coordinate[1,
+                                                                                 1]*temp[0, 1]+standby_coordinate[1, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 1, 1] = standby_coordinate[1, 0]*temp[1, 0]+standby_coordinate[1,
+                                                                                 1]*temp[1, 1]+standby_coordinate[1, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 1, 2] = standby_coordinate[1, 0]*temp[2, 0]+standby_coordinate[1,
+                                                                                 1]*temp[2, 1]+standby_coordinate[1, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 2, 0] = standby_coordinate[2, 0]*temp[0, 0]+standby_coordinate[2,
+                                                                                 1]*temp[0, 1]+standby_coordinate[2, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 2, 1] = standby_coordinate[2, 0]*temp[1, 0]+standby_coordinate[2,
+                                                                                 1]*temp[1, 1]+standby_coordinate[2, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 2, 2] = standby_coordinate[2, 0]*temp[2, 0]+standby_coordinate[2,
+                                                                                 1]*temp[2, 1]+standby_coordinate[2, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 3, 0] = standby_coordinate[3, 0]*temp[0, 0]+standby_coordinate[3,
+                                                                                 1]*temp[0, 1]+standby_coordinate[3, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 3, 1] = standby_coordinate[3, 0]*temp[1, 0]+standby_coordinate[3,
+                                                                                 1]*temp[1, 1]+standby_coordinate[3, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 3, 2] = standby_coordinate[3, 0]*temp[2, 0]+standby_coordinate[3,
+                                                                                 1]*temp[2, 1]+standby_coordinate[3, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 4, 0] = standby_coordinate[4, 0]*temp[0, 0]+standby_coordinate[4,
+                                                                                 1]*temp[0, 1]+standby_coordinate[4, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 4, 1] = standby_coordinate[4, 0]*temp[1, 0]+standby_coordinate[4,
+                                                                                 1]*temp[1, 1]+standby_coordinate[4, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 4, 2] = standby_coordinate[4, 0]*temp[2, 0]+standby_coordinate[4,
+                                                                                 1]*temp[2, 1]+standby_coordinate[4, 2]*temp[2, 2]+temp[2, 3]
+
+        path[idx, 5, 0] = standby_coordinate[5, 0]*temp[0, 0]+standby_coordinate[5,
+                                                                                 1]*temp[0, 1]+standby_coordinate[5, 2]*temp[0, 2]+temp[0, 3]
+        path[idx, 5, 1] = standby_coordinate[5, 0]*temp[1, 0]+standby_coordinate[5,
+                                                                                 1]*temp[1, 1]+standby_coordinate[5, 2]*temp[1, 2]+temp[1, 3]
+        path[idx, 5, 2] = standby_coordinate[5, 0]*temp[2, 0]+standby_coordinate[5,
+                                                                                 1]*temp[2, 1]+standby_coordinate[5, 2]*temp[2, 2]+temp[2, 3]
+
+    return path