forked from tangger/lerobot
547 lines
20 KiB
Python
547 lines
20 KiB
Python
# ruff: noqa: N806, N815, N803
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# Copyright 2024 The HuggingFace Inc. team. All rights reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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import numpy as np
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from scipy.spatial.transform import Rotation
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def skew_symmetric(w):
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"""Creates the skew-symmetric matrix from a 3D vector."""
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return np.array([[0, -w[2], w[1]], [w[2], 0, -w[0]], [-w[1], w[0], 0]])
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def rodrigues_rotation(w, theta):
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"""Computes the rotation matrix using Rodrigues' formula."""
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w_hat = skew_symmetric(w)
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return np.eye(3) + np.sin(theta) * w_hat + (1 - np.cos(theta)) * w_hat @ w_hat
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def screw_axis_to_transform(S, theta):
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"""Converts a screw axis to a 4x4 transformation matrix."""
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S_w = S[:3]
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S_v = S[3:]
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if np.allclose(S_w, 0) and np.linalg.norm(S_v) == 1: # Pure translation
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T = np.eye(4)
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T[:3, 3] = S_v * theta
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elif np.linalg.norm(S_w) == 1: # Rotation and translation
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w_hat = skew_symmetric(S_w)
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R = np.eye(3) + np.sin(theta) * w_hat + (1 - np.cos(theta)) * w_hat @ w_hat
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t = (np.eye(3) * theta + (1 - np.cos(theta)) * w_hat + (theta - np.sin(theta)) * w_hat @ w_hat) @ S_v
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T = np.eye(4)
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T[:3, :3] = R
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T[:3, 3] = t
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else:
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raise ValueError("Invalid screw axis parameters")
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return T
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def pose_difference_se3(pose1, pose2):
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"""
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Calculates the SE(3) difference between two 4x4 homogeneous transformation matrices.
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SE(3) (Special Euclidean Group) represents rigid body transformations in 3D space, combining rotation (SO(3)) and translation.
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Each 4x4 matrix has the following structure, a 3x3 rotation matrix in the top-left and a 3x1 translation vector in the top-right:
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[R11 R12 R13 tx]
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[R21 R22 R23 ty]
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[R31 R32 R33 tz]
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[ 0 0 0 1]
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where Rij is the 3x3 rotation matrix and [tx,ty,tz] is the translation vector.
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pose1 - pose2
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Args:
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pose1: A 4x4 numpy array representing the first pose.
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pose2: A 4x4 numpy array representing the second pose.
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Returns:
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A tuple (translation_diff, rotation_diff) where:
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- translation_diff is a 3x1 numpy array representing the translational difference.
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- rotation_diff is a 3x1 numpy array representing the rotational difference in axis-angle representation.
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"""
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# Extract rotation matrices from poses
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R1 = pose1[:3, :3]
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R2 = pose2[:3, :3]
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# Calculate translational difference
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translation_diff = pose1[:3, 3] - pose2[:3, 3]
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# Calculate rotational difference using scipy's Rotation library
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R_diff = Rotation.from_matrix(R1 @ R2.T)
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rotation_diff = R_diff.as_rotvec() # Convert to axis-angle representation
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return np.concatenate([translation_diff, rotation_diff])
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def se3_error(target_pose, current_pose):
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pos_error = target_pose[:3, 3] - current_pose[:3, 3]
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R_target = target_pose[:3, :3]
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R_current = current_pose[:3, :3]
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R_error = R_target @ R_current.T
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rot_error = Rotation.from_matrix(R_error).as_rotvec()
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return np.concatenate([pos_error, rot_error])
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class RobotKinematics:
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"""Robot kinematics class supporting multiple robot models."""
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# Robot measurements dictionary
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ROBOT_MEASUREMENTS = {
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"koch": {
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"gripper": [0.239, -0.001, 0.024],
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"wrist": [0.209, 0, 0.024],
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"forearm": [0.108, 0, 0.02],
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"humerus": [0, 0, 0.036],
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"shoulder": [0, 0, 0],
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"base": [0, 0, 0.02],
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},
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"so100": {
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"gripper": [0.320, 0, 0.050],
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"wrist": [0.278, 0, 0.050],
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"forearm": [0.143, 0, 0.044],
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"humerus": [0.031, 0, 0.072],
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"shoulder": [0, 0, 0],
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"base": [0, 0, 0.02],
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},
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"moss": {
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"gripper": [0.246, 0.013, 0.111],
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"wrist": [0.245, 0.002, 0.064],
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"forearm": [0.122, 0, 0.064],
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"humerus": [0.001, 0.001, 0.063],
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"shoulder": [0, 0, 0],
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"base": [0, 0, 0.02],
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},
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}
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def __init__(self, robot_type="so100"):
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"""Initialize kinematics for the specified robot type.
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Args:
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robot_type: String specifying the robot model ("koch", "so100", or "moss")
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"""
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if robot_type not in self.ROBOT_MEASUREMENTS:
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raise ValueError(
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f"Unknown robot type: {robot_type}. Available types: {list(self.ROBOT_MEASUREMENTS.keys())}"
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)
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self.robot_type = robot_type
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self.measurements = self.ROBOT_MEASUREMENTS[robot_type]
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# Initialize all transformation matrices and screw axes
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self._setup_transforms()
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def _create_translation_matrix(self, x=0, y=0, z=0):
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"""Create a 4x4 translation matrix."""
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return np.array([[1, 0, 0, x], [0, 1, 0, y], [0, 0, 1, z], [0, 0, 0, 1]])
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def _setup_transforms(self):
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"""Setup all transformation matrices and screw axes for the robot."""
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# Set up rotation matrices (constant across robot types)
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# Gripper orientation
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self.gripper_X0 = np.array(
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[
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[1, 0, 0, 0],
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[0, 0, 1, 0],
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[0, -1, 0, 0],
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[0, 0, 0, 1],
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]
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)
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# Wrist orientation
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self.wrist_X0 = np.array(
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[
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[0, -1, 0, 0],
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[1, 0, 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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)
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# Base orientation
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self.base_X0 = np.array(
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[
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[0, 0, 1, 0],
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[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 0, 1],
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]
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)
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# Gripper
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# Screw axis of gripper frame wrt base frame
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self.S_BG = np.array(
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[
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1,
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0,
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0,
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0,
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self.measurements["gripper"][2],
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-self.measurements["gripper"][1],
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]
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)
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# Gripper origin to centroid transform
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self.X_GoGc = self._create_translation_matrix(x=0.07)
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# Gripper origin to tip transform
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self.X_GoGt = self._create_translation_matrix(x=0.12)
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# 0-position gripper frame pose wrt base
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self.X_BoGo = self._create_translation_matrix(
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x=self.measurements["gripper"][0],
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y=self.measurements["gripper"][1],
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z=self.measurements["gripper"][2],
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)
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# Wrist
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# Screw axis of wrist frame wrt base frame
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self.S_BR = np.array([0, 1, 0, -self.measurements["wrist"][2], 0, self.measurements["wrist"][0]])
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# 0-position origin to centroid transform
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self.X_RoRc = self._create_translation_matrix(x=0.0035, y=-0.002)
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# 0-position wrist frame pose wrt base
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self.X_BR = self._create_translation_matrix(
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x=self.measurements["wrist"][0],
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y=self.measurements["wrist"][1],
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z=self.measurements["wrist"][2],
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)
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# Forearm
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# Screw axis of forearm frame wrt base frame
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self.S_BF = np.array(
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[
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0,
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1,
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0,
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-self.measurements["forearm"][2],
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0,
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self.measurements["forearm"][0],
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]
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)
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# Forearm origin + centroid transform
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self.X_FoFc = self._create_translation_matrix(x=0.036) # spellchecker:disable-line
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# 0-position forearm frame pose wrt base
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self.X_BF = self._create_translation_matrix(
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x=self.measurements["forearm"][0],
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y=self.measurements["forearm"][1],
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z=self.measurements["forearm"][2],
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)
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# Humerus
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# Screw axis of humerus frame wrt base frame
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self.S_BH = np.array(
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[
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0,
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-1,
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0,
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self.measurements["humerus"][2],
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0,
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-self.measurements["humerus"][0],
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]
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)
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# Humerus origin to centroid transform
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self.X_HoHc = self._create_translation_matrix(x=0.0475)
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# 0-position humerus frame pose wrt base
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self.X_BH = self._create_translation_matrix(
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x=self.measurements["humerus"][0],
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y=self.measurements["humerus"][1],
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z=self.measurements["humerus"][2],
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)
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# Shoulder
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# Screw axis of shoulder frame wrt Base frame
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self.S_BS = np.array([0, 0, -1, 0, 0, 0])
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# Shoulder origin to centroid transform
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self.X_SoSc = self._create_translation_matrix(x=-0.017, z=0.0235)
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# 0-position shoulder frame pose wrt base
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self.X_BS = self._create_translation_matrix(
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x=self.measurements["shoulder"][0],
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y=self.measurements["shoulder"][1],
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z=self.measurements["shoulder"][2],
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)
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# Base
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# Base origin to centroid transform
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self.X_BoBc = self._create_translation_matrix(y=0.015)
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# World to base transform
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self.X_WoBo = self._create_translation_matrix(
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x=self.measurements["base"][0],
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y=self.measurements["base"][1],
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z=self.measurements["base"][2],
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)
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# Pre-compute gripper post-multiplication matrix
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self._fk_gripper_post = self.X_GoGc @ self.X_BoGo @ self.gripper_X0
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def fk_base(self):
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"""Forward kinematics for the base frame."""
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return self.X_WoBo @ self.X_BoBc @ self.base_X0
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def fk_shoulder(self, robot_pos_deg):
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"""Forward kinematics for the shoulder frame."""
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robot_pos_rad = robot_pos_deg / 180 * np.pi
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return self.X_WoBo @ screw_axis_to_transform(self.S_BS, robot_pos_rad[0]) @ self.X_SoSc @ self.X_BS
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def fk_humerus(self, robot_pos_deg):
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"""Forward kinematics for the humerus frame."""
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robot_pos_rad = robot_pos_deg / 180 * np.pi
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return (
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self.X_WoBo
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@ screw_axis_to_transform(self.S_BS, robot_pos_rad[0])
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@ screw_axis_to_transform(self.S_BH, robot_pos_rad[1])
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@ self.X_HoHc
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@ self.X_BH
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)
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def fk_forearm(self, robot_pos_deg):
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"""Forward kinematics for the forearm frame."""
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robot_pos_rad = robot_pos_deg / 180 * np.pi
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return (
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self.X_WoBo
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@ screw_axis_to_transform(self.S_BS, robot_pos_rad[0])
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@ screw_axis_to_transform(self.S_BH, robot_pos_rad[1])
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@ screw_axis_to_transform(self.S_BF, robot_pos_rad[2])
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@ self.X_FoFc # spellchecker:disable-line
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@ self.X_BF
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)
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def fk_wrist(self, robot_pos_deg):
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"""Forward kinematics for the wrist frame."""
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robot_pos_rad = robot_pos_deg / 180 * np.pi
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return (
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self.X_WoBo
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@ screw_axis_to_transform(self.S_BS, robot_pos_rad[0])
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@ screw_axis_to_transform(self.S_BH, robot_pos_rad[1])
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@ screw_axis_to_transform(self.S_BF, robot_pos_rad[2])
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@ screw_axis_to_transform(self.S_BR, robot_pos_rad[3])
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@ self.X_RoRc
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@ self.X_BR
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@ self.wrist_X0
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)
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def fk_gripper(self, robot_pos_deg):
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"""Forward kinematics for the gripper frame."""
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robot_pos_rad = robot_pos_deg / 180 * np.pi
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return (
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self.X_WoBo
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@ screw_axis_to_transform(self.S_BS, robot_pos_rad[0])
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@ screw_axis_to_transform(self.S_BH, robot_pos_rad[1])
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@ screw_axis_to_transform(self.S_BF, robot_pos_rad[2])
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@ screw_axis_to_transform(self.S_BR, robot_pos_rad[3])
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@ screw_axis_to_transform(self.S_BG, robot_pos_rad[4])
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@ self._fk_gripper_post
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)
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def fk_gripper_tip(self, robot_pos_deg):
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"""Forward kinematics for the gripper tip frame."""
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robot_pos_rad = robot_pos_deg / 180 * np.pi
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return (
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self.X_WoBo
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@ screw_axis_to_transform(self.S_BS, robot_pos_rad[0])
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@ screw_axis_to_transform(self.S_BH, robot_pos_rad[1])
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@ screw_axis_to_transform(self.S_BF, robot_pos_rad[2])
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@ screw_axis_to_transform(self.S_BR, robot_pos_rad[3])
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@ screw_axis_to_transform(self.S_BG, robot_pos_rad[4])
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@ self.X_GoGt
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@ self.X_BoGo
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@ self.gripper_X0
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)
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def compute_jacobian(self, robot_pos_deg, fk_func=None):
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"""Finite differences to compute the Jacobian.
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J(i, j) represents how the ith component of the end-effector's velocity changes wrt a small change
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in the jth joint's velocity.
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Args:
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robot_pos_deg: Current joint positions in degrees
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fk_func: Forward kinematics function to use (defaults to fk_gripper)
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"""
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if fk_func is None:
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fk_func = self.fk_gripper
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eps = 1e-8
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jac = np.zeros(shape=(6, 5))
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delta = np.zeros(len(robot_pos_deg[:-1]), dtype=np.float64)
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for el_ix in range(len(robot_pos_deg[:-1])):
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delta *= 0
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delta[el_ix] = eps / 2
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Sdot = (
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pose_difference_se3(
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fk_func(robot_pos_deg[:-1] + delta),
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fk_func(robot_pos_deg[:-1] - delta),
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)
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/ eps
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)
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jac[:, el_ix] = Sdot
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return jac
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def compute_positional_jacobian(self, robot_pos_deg, fk_func=None):
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"""Finite differences to compute the positional Jacobian.
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J(i, j) represents how the ith component of the end-effector's position changes wrt a small change
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in the jth joint's velocity.
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Args:
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robot_pos_deg: Current joint positions in degrees
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fk_func: Forward kinematics function to use (defaults to fk_gripper)
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"""
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if fk_func is None:
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fk_func = self.fk_gripper
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eps = 1e-8
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jac = np.zeros(shape=(3, 5))
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delta = np.zeros(len(robot_pos_deg[:-1]), dtype=np.float64)
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for el_ix in range(len(robot_pos_deg[:-1])):
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delta *= 0
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delta[el_ix] = eps / 2
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Sdot = (
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fk_func(robot_pos_deg[:-1] + delta)[:3, 3] - fk_func(robot_pos_deg[:-1] - delta)[:3, 3]
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) / eps
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jac[:, el_ix] = Sdot
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return jac
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def ik(self, current_joint_state, desired_ee_pose, position_only=True, fk_func=None):
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"""Inverse kinematics using gradient descent.
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Args:
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current_joint_state: Initial joint positions in degrees
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desired_ee_pose: Target end-effector pose as a 4x4 transformation matrix
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position_only: If True, only match end-effector position, not orientation
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fk_func: Forward kinematics function to use (defaults to fk_gripper)
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Returns:
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Joint positions in degrees that achieve the desired end-effector pose
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"""
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if fk_func is None:
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fk_func = self.fk_gripper
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# Do gradient descent.
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max_iterations = 5
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learning_rate = 1
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for _ in range(max_iterations):
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current_ee_pose = fk_func(current_joint_state)
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if not position_only:
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error = se3_error(desired_ee_pose, current_ee_pose)
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jac = self.compute_jacobian(current_joint_state, fk_func)
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else:
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error = desired_ee_pose[:3, 3] - current_ee_pose[:3, 3]
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jac = self.compute_positional_jacobian(current_joint_state, fk_func)
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delta_angles = np.linalg.pinv(jac) @ error
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current_joint_state[:-1] += learning_rate * delta_angles
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if np.linalg.norm(error) < 5e-3:
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return current_joint_state
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return current_joint_state
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if __name__ == "__main__":
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import time
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def run_test(robot_type):
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"""Run test suite for a specific robot type."""
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print(f"\n--- Testing {robot_type.upper()} Robot ---")
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# Initialize kinematics for this robot
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robot = RobotKinematics(robot_type)
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# Test 1: Forward kinematics consistency
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print("Test 1: Forward kinematics consistency")
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test_angles = np.array([30, 45, -30, 20, 10, 0]) # Example joint angles in degrees
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# Calculate FK for different joints
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shoulder_pose = robot.fk_shoulder(test_angles)
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humerus_pose = robot.fk_humerus(test_angles)
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forearm_pose = robot.fk_forearm(test_angles)
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wrist_pose = robot.fk_wrist(test_angles)
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gripper_pose = robot.fk_gripper(test_angles)
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gripper_tip_pose = robot.fk_gripper_tip(test_angles)
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# Check that poses form a consistent kinematic chain (positions should be progressively further from origin)
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distances = [
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np.linalg.norm(shoulder_pose[:3, 3]),
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np.linalg.norm(humerus_pose[:3, 3]),
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np.linalg.norm(forearm_pose[:3, 3]),
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np.linalg.norm(wrist_pose[:3, 3]),
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np.linalg.norm(gripper_pose[:3, 3]),
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np.linalg.norm(gripper_tip_pose[:3, 3]),
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]
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# Check if distances generally increase along the chain
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is_consistent = all(distances[i] <= distances[i + 1] for i in range(len(distances) - 1))
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print(f" Pose distances from origin: {[round(d, 3) for d in distances]}")
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print(f" Kinematic chain consistency: {'PASSED' if is_consistent else 'FAILED'}")
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# Test 2: Jacobian computation
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print("Test 2: Jacobian computation")
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jacobian = robot.compute_jacobian(test_angles)
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positional_jacobian = robot.compute_positional_jacobian(test_angles)
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# Check shapes
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jacobian_shape_ok = jacobian.shape == (6, 5)
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pos_jacobian_shape_ok = positional_jacobian.shape == (3, 5)
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print(f" Jacobian shape: {'PASSED' if jacobian_shape_ok else 'FAILED'}")
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print(f" Positional Jacobian shape: {'PASSED' if pos_jacobian_shape_ok else 'FAILED'}")
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# Test 3: Inverse kinematics
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print("Test 3: Inverse kinematics (position only)")
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# Generate target pose from known joint angles
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original_angles = np.array([10, 20, 30, -10, 5, 0])
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target_pose = robot.fk_gripper(original_angles)
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# Start IK from a different position
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initial_guess = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
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# Measure IK performance
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start_time = time.time()
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computed_angles = robot.ik(initial_guess.copy(), target_pose)
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ik_time = time.time() - start_time
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# Compute resulting pose from IK solution
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result_pose = robot.fk_gripper(computed_angles)
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# Calculate position error
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pos_error = np.linalg.norm(target_pose[:3, 3] - result_pose[:3, 3])
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passed = pos_error < 0.01 # Accept errors less than 1cm
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print(f" IK computation time: {ik_time:.4f} seconds")
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print(f" Position error: {pos_error:.4f}")
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print(f" IK position accuracy: {'PASSED' if passed else 'FAILED'}")
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return is_consistent and jacobian_shape_ok and pos_jacobian_shape_ok and passed
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# Run tests for all robot types
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results = {}
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for robot_type in ["koch", "so100", "moss"]:
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results[robot_type] = run_test(robot_type)
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# Print overall summary
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print("\n=== Test Summary ===")
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all_passed = all(results.values())
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for robot_type, passed in results.items():
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print(f"{robot_type.upper()}: {'PASSED' if passed else 'FAILED'}")
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print(f"\nOverall: {'ALL TESTS PASSED' if all_passed else 'SOME TESTS FAILED'}")
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