🦴 Adds Simulator from OpenQuadruped/spot_mini_mini
This commit is contained in:
Rune Harlyk
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#!/usr/bin/env python
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# https://www.researchgate.net/publication/320307716_Inverse_Kinematic_Analysis_Of_A_Quadruped_Robot
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import numpy as np
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class LegIK():
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def __init__(self,
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legtype="RIGHT",
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shoulder_length=0.04,
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elbow_length=0.1,
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wrist_length=0.125,
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hip_lim=[-0.548, 0.548],
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shoulder_lim=[-2.17, 0.97],
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leg_lim=[-0.1, 2.59]):
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self.legtype = legtype
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self.shoulder_length = shoulder_length
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self.elbow_length = elbow_length
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self.wrist_length = wrist_length
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self.hip_lim = hip_lim
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self.shoulder_lim = shoulder_lim
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self.leg_lim = leg_lim
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def get_domain(self, x, y, z):
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"""
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Calculates the leg's Domain and caps it in case of a breach
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:param x,y,z: hip-to-foot distances in each dimension
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:return: Leg Domain D
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"""
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D = (y**2 + (-z)**2 - self.shoulder_length**2 +
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(-x)**2 - self.elbow_length**2 - self.wrist_length**2) / (
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2 * self.wrist_length * self.elbow_length)
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if D > 1 or D < -1:
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# DOMAIN BREACHED
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# print("---------DOMAIN BREACH---------")
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D = np.clip(D, -1.0, 1.0)
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return D
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else:
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return D
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def solve(self, xyz_coord):
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"""
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Generic Leg Inverse Kinematics Solver
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:param xyz_coord: hip-to-foot distances in each dimension
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:return: Joint Angles required for desired position
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"""
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x = xyz_coord[0]
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y = xyz_coord[1]
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z = xyz_coord[2]
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D = self.get_domain(x, y, z)
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if self.legtype == "RIGHT":
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return self.RightIK(x, y, z, D)
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else:
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return self.LeftIK(x, y, z, D)
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def RightIK(self, x, y, z, D):
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"""
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Right Leg Inverse Kinematics Solver
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:param x,y,z: hip-to-foot distances in each dimension
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:param D: leg domain
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:return: Joint Angles required for desired position
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"""
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wrist_angle = np.arctan2(-np.sqrt(1 - D**2), D)
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sqrt_component = y**2 + (-z)**2 - self.shoulder_length**2
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if sqrt_component < 0.0:
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# print("NEGATIVE SQRT")
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sqrt_component = 0.0
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shoulder_angle = -np.arctan2(z, y) - np.arctan2(
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np.sqrt(sqrt_component), -self.shoulder_length)
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elbow_angle = np.arctan2(-x, np.sqrt(sqrt_component)) - np.arctan2(
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self.wrist_length * np.sin(wrist_angle),
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self.elbow_length + self.wrist_length * np.cos(wrist_angle))
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joint_angles = np.array([-shoulder_angle, elbow_angle, wrist_angle])
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return joint_angles
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def LeftIK(self, x, y, z, D):
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"""
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Left Leg Inverse Kinematics Solver
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:param x,y,z: hip-to-foot distances in each dimension
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:param D: leg domain
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:return: Joint Angles required for desired position
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"""
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wrist_angle = np.arctan2(-np.sqrt(1 - D**2), D)
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sqrt_component = y**2 + (-z)**2 - self.shoulder_length**2
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if sqrt_component < 0.0:
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print("NEGATIVE SQRT")
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sqrt_component = 0.0
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shoulder_angle = -np.arctan2(z, y) - np.arctan2(
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np.sqrt(sqrt_component), self.shoulder_length)
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elbow_angle = np.arctan2(-x, np.sqrt(sqrt_component)) - np.arctan2(
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self.wrist_length * np.sin(wrist_angle),
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self.elbow_length + self.wrist_length * np.cos(wrist_angle))
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joint_angles = np.array([-shoulder_angle, elbow_angle, wrist_angle])
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return joint_angles
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@@ -0,0 +1,182 @@
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#!/usr/bin/env python
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import numpy as np
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# NOTE: Code snippets from Modern Robotics at Northwestern University:
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# See https://github.com/NxRLab/ModernRobotics
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def RpToTrans(R, p):
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"""
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Converts a rotation matrix and a position vector into homogeneous
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transformation matrix
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:param R: A 3x3 rotation matrix
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:param p: A 3-vector
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:return: A homogeneous transformation matrix corresponding to the inputs
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Example Input:
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R = np.array([[1, 0, 0],
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[0, 0, -1],
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[0, 1, 0]])
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p = np.array([1, 2, 5])
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Output:
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np.array([[1, 0, 0, 1],
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[0, 0, -1, 2],
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[0, 1, 0, 5],
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[0, 0, 0, 1]])
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"""
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return np.r_[np.c_[R, p], [[0, 0, 0, 1]]]
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def TransToRp(T):
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"""
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Converts a homogeneous transformation matrix into a rotation matrix
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and position vector
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:param T: A homogeneous transformation matrix
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:return R: The corresponding rotation matrix,
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:return p: The corresponding position vector.
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Example Input:
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T = np.array([[1, 0, 0, 0],
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[0, 0, -1, 0],
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[0, 1, 0, 3],
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[0, 0, 0, 1]])
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Output:
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(np.array([[1, 0, 0],
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[0, 0, -1],
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[0, 1, 0]]),
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np.array([0, 0, 3]))
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"""
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T = np.array(T)
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return T[0:3, 0:3], T[0:3, 3]
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def TransInv(T):
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"""
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Inverts a homogeneous transformation matrix
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:param T: A homogeneous transformation matrix
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:return: The inverse of T
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Uses the structure of transformation matrices to avoid taking a matrix
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inverse, for efficiency.
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Example input:
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T = np.array([[1, 0, 0, 0],
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[0, 0, -1, 0],
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[0, 1, 0, 3],
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[0, 0, 0, 1]])
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Output:
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np.array([[1, 0, 0, 0],
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[0, 0, 1, -3],
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[0, -1, 0, 0],
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[0, 0, 0, 1]])
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"""
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R, p = TransToRp(T)
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Rt = np.array(R).T
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return np.r_[np.c_[Rt, -np.dot(Rt, p)], [[0, 0, 0, 1]]]
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def Adjoint(T):
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"""
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Computes the adjoint representation of a homogeneous transformation
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matrix
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:param T: A homogeneous transformation matrix
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:return: The 6x6 adjoint representation [AdT] of T
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Example Input:
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T = np.array([[1, 0, 0, 0],
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[0, 0, -1, 0],
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[0, 1, 0, 3],
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[0, 0, 0, 1]])
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Output:
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np.array([[1, 0, 0, 0, 0, 0],
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[0, 0, -1, 0, 0, 0],
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[0, 1, 0, 0, 0, 0],
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[0, 0, 3, 1, 0, 0],
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[3, 0, 0, 0, 0, -1],
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[0, 0, 0, 0, 1, 0]])
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"""
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R, p = TransToRp(T)
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return np.r_[np.c_[R, np.zeros((3, 3))], np.c_[np.dot(VecToso3(p), R), R]]
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def VecToso3(omg):
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"""
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Converts a 3-vector to an so(3) representation
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:param omg: A 3-vector
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:return: The skew symmetric representation of omg
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Example Input:
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omg = np.array([1, 2, 3])
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Output:
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np.array([[ 0, -3, 2],
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[ 3, 0, -1],
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[-2, 1, 0]])
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"""
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return np.array([[0, -omg[2], omg[1]], [omg[2], 0, -omg[0]],
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[-omg[1], omg[0], 0]])
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def RPY(roll, pitch, yaw):
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"""
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Creates a Roll, Pitch, Yaw Transformation Matrix
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:param roll: roll component of matrix
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:param pitch: pitch component of matrix
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:param yaw: yaw component of matrix
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:return: The transformation matrix
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Example Input:
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roll = 0.0
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pitch = 0.0
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yaw = 0.0
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Output:
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np.array([[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]])
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"""
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Roll = np.array([[1, 0, 0, 0], [0, np.cos(roll), -np.sin(roll), 0],
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[0, np.sin(roll), np.cos(roll), 0], [0, 0, 0, 1]])
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Pitch = np.array([[np.cos(pitch), 0, np.sin(pitch), 0], [0, 1, 0, 0],
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[-np.sin(pitch), 0, np.cos(pitch), 0], [0, 0, 0, 1]])
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Yaw = np.array([[np.cos(yaw), -np.sin(yaw), 0, 0],
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[np.sin(yaw), np.cos(yaw), 0, 0], [0, 0, 1, 0],
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[0, 0, 0, 1]])
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return np.matmul(np.matmul(Roll, Pitch), Yaw)
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def RotateTranslate(rotation, position):
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"""
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Creates a Transformation Matrix from a Rotation, THEN, a Translation
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:param rotation: pure rotation matrix
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:param translation: pure translation matrix
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:return: The transformation matrix
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"""
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trans = np.eye(4)
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trans[0, 3] = position[0]
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trans[1, 3] = position[1]
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trans[2, 3] = position[2]
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return np.dot(rotation, trans)
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def TransformVector(xyz_coord, rotation, translation):
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"""
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Transforms a vector by a specified Rotation THEN Translation Matrix
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:param xyz_coord: the vector to transform
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:param rotation: pure rotation matrix
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:param translation: pure translation matrix
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:return: The transformed vector
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"""
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xyz_vec = np.append(xyz_coord, 1.0)
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Transformed = np.dot(RotateTranslate(rotation, translation), xyz_vec)
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return Transformed[:3]
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@@ -0,0 +1,224 @@
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#!/usr/bin/env python
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import numpy as np
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from Kinematics.LegKinematics import LegIK
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from Kinematics.LieAlgebra import RpToTrans, TransToRp, TransInv, RPY, TransformVector
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from collections import OrderedDict
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class SpotModel:
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def __init__(
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self,
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shoulder_length=0.055,
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elbow_length=0.10652,
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wrist_length=0.145,
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hip_x=0.23,
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hip_y=0.075,
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foot_x=0.23,
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foot_y=0.185,
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height=0.20,
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com_offset=0.016,
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shoulder_lim=[-0.548, 0.548],
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elbow_lim=[-2.17, 0.97],
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wrist_lim=[-0.1, 2.59],
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):
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"""
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Spot Micro Kinematics
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"""
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# COM offset in x direction
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self.com_offset = com_offset
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# Leg Parameters
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self.shoulder_length = shoulder_length
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self.elbow_length = elbow_length
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self.wrist_length = wrist_length
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# Leg Vector desired_positions
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# Distance Between Hips
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# Length
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self.hip_x = hip_x
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# Width
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self.hip_y = hip_y
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# Distance Between Feet
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# Length
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self.foot_x = foot_x
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# Width
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self.foot_y = foot_y
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# Body Height
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self.height = height
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# Joint Parameters
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self.shoulder_lim = shoulder_lim
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self.elbow_lim = elbow_lim
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self.wrist_lim = wrist_lim
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# Dictionary to store Leg IK Solvers
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self.Legs = OrderedDict()
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self.Legs["FL"] = LegIK(
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"LEFT",
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self.shoulder_length,
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self.elbow_length,
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self.wrist_length,
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self.shoulder_lim,
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self.elbow_lim,
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self.wrist_lim,
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)
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self.Legs["FR"] = LegIK(
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"RIGHT",
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self.shoulder_length,
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self.elbow_length,
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self.wrist_length,
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self.shoulder_lim,
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self.elbow_lim,
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self.wrist_lim,
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)
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self.Legs["BL"] = LegIK(
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"LEFT",
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self.shoulder_length,
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self.elbow_length,
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self.wrist_length,
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self.shoulder_lim,
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self.elbow_lim,
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self.wrist_lim,
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)
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self.Legs["BR"] = LegIK(
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"RIGHT",
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self.shoulder_length,
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self.elbow_length,
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self.wrist_length,
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self.shoulder_lim,
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self.elbow_lim,
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self.wrist_lim,
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)
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# Dictionary to store Hip and Foot Transforms
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# Transform of Hip relative to world frame
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# With Body Centroid also in world frame
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Rwb = np.eye(3)
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self.WorldToHip = OrderedDict()
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self.ph_FL = np.array([self.hip_x / 2.0, self.hip_y / 2.0, 0])
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self.WorldToHip["FL"] = RpToTrans(Rwb, self.ph_FL)
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self.ph_FR = np.array([self.hip_x / 2.0, -self.hip_y / 2.0, 0])
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self.WorldToHip["FR"] = RpToTrans(Rwb, self.ph_FR)
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self.ph_BL = np.array([-self.hip_x / 2.0, self.hip_y / 2.0, 0])
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self.WorldToHip["BL"] = RpToTrans(Rwb, self.ph_BL)
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self.ph_BR = np.array([-self.hip_x / 2.0, -self.hip_y / 2.0, 0])
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self.WorldToHip["BR"] = RpToTrans(Rwb, self.ph_BR)
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# Transform of Foot relative to world frame
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# With Body Centroid also in world frame
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self.WorldToFoot = OrderedDict()
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self.pf_FL = np.array([self.foot_x / 2.0, self.foot_y / 2.0, -self.height])
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self.WorldToFoot["FL"] = RpToTrans(Rwb, self.pf_FL)
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self.pf_FR = np.array([self.foot_x / 2.0, -self.foot_y / 2.0, -self.height])
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self.WorldToFoot["FR"] = RpToTrans(Rwb, self.pf_FR)
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self.pf_BL = np.array([-self.foot_x / 2.0, self.foot_y / 2.0, -self.height])
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self.WorldToFoot["BL"] = RpToTrans(Rwb, self.pf_BL)
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self.pf_BR = np.array([-self.foot_x / 2.0, -self.foot_y / 2.0, -self.height])
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self.WorldToFoot["BR"] = RpToTrans(Rwb, self.pf_BR)
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def HipToFoot(self, orn, pos, T_bf):
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"""
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Converts a desired position and orientation wrt Spot's
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home position, with a desired body-to-foot Transform
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into a body-to-hip Transform, which is used to extract
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and return the Hip To Foot Vector.
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:param orn: A 3x1 np.array([]) with Spot's Roll, Pitch, Yaw angles
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:param pos: A 3x1 np.array([]) with Spot's X, Y, Z coordinates
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:param T_bf: Dictionary of desired body-to-foot Transforms.
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:return: Hip To Foot Vector for each of Spot's Legs.
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"""
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# Following steps in attached document: SpotBodyIK.
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# TODO: LINK DOC
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# Only get Rot component
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Rb, _ = TransToRp(RPY(orn[0], orn[1], orn[2]))
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pb = pos
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T_wb = RpToTrans(Rb, pb)
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# Dictionary to store vectors
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HipToFoot_List = OrderedDict()
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for i, (key, T_wh) in enumerate(self.WorldToHip.items()):
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# ORDER: FL, FR, FR, BL, BR
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# Extract vector component
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_, p_bf = TransToRp(T_bf[key])
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# Step 1, get T_bh for each leg
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T_bh = np.dot(TransInv(T_wb), T_wh)
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# Step 2, get T_hf for each leg
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# VECTOR ADDITION METHOD
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_, p_bh = TransToRp(T_bh)
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p_hf0 = p_bf - p_bh
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# TRANSFORM METHOD
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T_hf = np.dot(TransInv(T_bh), T_bf[key])
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_, p_hf1 = TransToRp(T_hf)
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# They should yield the same result
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if p_hf1.all() != p_hf0.all():
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print("NOT EQUAL")
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p_hf = p_hf1
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HipToFoot_List[key] = p_hf
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return HipToFoot_List
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def IK(self, orn, pos, T_bf):
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"""
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Uses HipToFoot() to convert a desired position
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and orientation wrt Spot's home position into a
|
||||
Hip To Foot Vector, which is fed into the LegIK solver.
|
||||
|
||||
Finally, the resultant joint angles are returned
|
||||
from the LegIK solver for each leg.
|
||||
|
||||
:param orn: A 3x1 np.array([]) with Spot's Roll, Pitch, Yaw angles
|
||||
:param pos: A 3x1 np.array([]) with Spot's X, Y, Z coordinates
|
||||
:param T_bf: Dictionary of desired body-to-foot Transforms.
|
||||
:return: Joint angles for each of Spot's joints.
|
||||
"""
|
||||
|
||||
# Following steps in attached document: SpotBodyIK.
|
||||
# TODO: LINK DOC
|
||||
|
||||
# Modify x by com offset
|
||||
pos[0] += self.com_offset
|
||||
|
||||
# 4 legs, 3 joints per leg
|
||||
joint_angles = np.zeros((4, 3))
|
||||
|
||||
# print("T_bf: {}".format(T_bf))
|
||||
|
||||
# Steps 1 and 2 of pipeline here
|
||||
HipToFoot = self.HipToFoot(orn, pos, T_bf)
|
||||
|
||||
for i, (key, p_hf) in enumerate(HipToFoot.items()):
|
||||
# ORDER: FL, FR, FR, BL, BR
|
||||
|
||||
# print("LEG: {} \t HipToFoot: {}".format(key, p_hf))
|
||||
|
||||
# Step 3, compute joint angles from T_hf for each leg
|
||||
joint_angles[i, :] = self.Legs[key].solve(p_hf)
|
||||
|
||||
# print("-----------------------------")
|
||||
|
||||
return joint_angles
|
||||
Reference in New Issue
Block a user