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‎README.md

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@@ -70,58 +70,58 @@ import roboticstoolbox as rtb
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robot = rtb.models.DH.Panda()
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print(robot)
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┏━━━━━━━━┳━━━━━━━━┳━━━━━┳━━━━━━━┳━━━━━━━━━┳━━━━━━━━┓
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┃ aⱼ₋₁ ┃ ⍺ⱼ₋₁ ┃ θⱼ ┃ dⱼ ┃ q⁻ ┃ q⁺ ┃
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┣━━━━━━━━╋━━━━━━━━╋━━━━━╋━━━━━━━╋━━━━━━━━━╋━━━━━━━━┫
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┃ 0.0 ┃ 0.0° ┃ q1 ┃ 0.333 ┃ -166.0° ┃ 166.0° ┃
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┃ 0.0 ┃ -90.0° ┃ q2 ┃ 0.0 ┃ -101.0° ┃ 101.0° ┃
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┃ 0.0 ┃ 90.0° ┃ q3 ┃ 0.316 ┃ -166.0° ┃ 166.0° ┃
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┃ 0.0825 ┃ 90.0° ┃ q4 ┃ 0.0 ┃ -176.0° ┃ -4.0° ┃
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┃-0.0825 ┃ -90.0° ┃ q5 ┃ 0.384 ┃ -166.0° ┃ 166.0° ┃
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┃ 0.0 ┃ 90.0° ┃ q6 ┃ 0.0 ┃ -1.0° ┃ 215.0° ┃
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┃ 0.088 ┃ 90.0° ┃ q7 ┃ 0.107 ┃ -166.0° ┃ 166.0° ┃
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┗━━━━━━━━┻━━━━━━━━┻━━━━━┻━━━━━━━┻━━━━━━━━━┻━━━━━━━━┛
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┌─────┬───────────────────────────────────────┐
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│tool │ t = 0, 0, 0.1; rpy/xyz = -45°, 0°, 0° │
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└─────┴───────────────────────────────────────┘
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┌─────┬─────┬────────┬─────┬───────┬─────┬───────┬──────┐
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│name │ q0 │ q1 │ q2 │ q3 │ q4 │ q5 │ q6 │
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├─────┼─────┼────────┼─────┼───────┼─────┼───────┼──────┤
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│ qz │ 0° │ 0° │ 0° │ 0° │ 0° │ 0° │ 0° │
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│ qr │ 0° │ -17.2° │ 0° │ -126° │ 0° │ 115° │ 45° │
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└─────┴─────┴────────┴─────┴───────┴─────┴───────┴──────┘
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┏━━━━━━━━┳━━━━━━━━┳━━━━━┳━━━━━━━┳━━━━━━━━━┳━━━━━━━━┓
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┃ aⱼ₋₁ ┃ ⍺ⱼ₋₁ ┃ θⱼ ┃ dⱼ ┃ q⁻ ┃ q⁺ ┃
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┣━━━━━━━━╋━━━━━━━━╋━━━━━╋━━━━━━━╋━━━━━━━━━╋━━━━━━━━┫
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┃ 0.0 ┃ 0.0° ┃ q1 ┃ 0.333 ┃ -166.0° ┃ 166.0° ┃
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┃ 0.0 ┃ -90.0° ┃ q2 ┃ 0.0 ┃ -101.0° ┃ 101.0° ┃
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┃ 0.0 ┃ 90.0° ┃ q3 ┃ 0.316 ┃ -166.0° ┃ 166.0° ┃
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┃ 0.0825 ┃ 90.0° ┃ q4 ┃ 0.0 ┃ -176.0° ┃ -4.0° ┃
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┃-0.0825 ┃ -90.0° ┃ q5 ┃ 0.384 ┃ -166.0° ┃ 166.0° ┃
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┃ 0.0 ┃ 90.0° ┃ q6 ┃ 0.0 ┃ -1.0° ┃ 215.0° ┃
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┃ 0.088 ┃ 90.0° ┃ q7 ┃ 0.107 ┃ -166.0° ┃ 166.0° ┃
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┗━━━━━━━━┻━━━━━━━━┻━━━━━┻━━━━━━━┻━━━━━━━━━┻━━━━━━━━┛
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┌─────┬───────────────────────────────────────┐
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│tool │ t = 0, 0, 0.1; rpy/xyz = -45°, 0°, 0° │
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└─────┴───────────────────────────────────────┘
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┌─────┬─────┬────────┬─────┬───────┬─────┬───────┬──────┐
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│name │ q0 │ q1 │ q2 │ q3 │ q4 │ q5 │ q6 │
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├─────┼─────┼────────┼─────┼───────┼─────┼───────┼──────┤
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│ qz │ 0° │ 0° │ 0° │ 0° │ 0° │ 0° │ 0° │
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│ qr │ 0° │ -17.2° │ 0° │ -126° │ 0° │ 115° │ 45° │
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└─────┴─────┴────────┴─────┴───────┴─────┴───────┴──────┘
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T = robot.fkine(robot.qz) # forward kinematics
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print(T)
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0.707107 0.707107 0 0.088
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0.707107 -0.707107 0 0
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0 0 -1 0.823
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0 0 0 1
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0.707107 0.707107 0 0.088
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0.707107 -0.707107 0 0
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0 0 -1 0.823
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0 0 0 1
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```
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(Python prompts are not shown to make it easy to copy+paste the code)
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(Python prompts are not shown to make it easy to copy+paste the code, console output is indented)
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We can solve inverse kinematics very easily. We first choose an SE(3) pose
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defined in terms of position and orientation (end-effector z-axis down (-Z) and finger
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orientation (+Y)).
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defined in terms of position and orientation (end-effector z-axis down (A=-Z) and finger
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orientation parallel to y-axis (O=+Y)).
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```python
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from spatialmath import SE3
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T = SE3(0.8, 0.2, 0.1) * SE3.OA([0, 1, 0], [0, 0, -1])
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q_pickup, *_ = robot.ikine(T) # solve IK, ignore additional outputs
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q_pickup, *_ = robot.ikunc(T) # solve IK, ignore additional outputs
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print(q_pickup) # display joint angles
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[ 1.10903519 1.21806211 0.10114796 1.49547496 0.33270093 -0.29437262 -0.8927488 ]
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[ 1.10903519 1.21806211 0.10114796 1.49547496 0.33270093 -0.29437262 -0.8927488 ]
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print(robot.fkine(q_pickup)) # FK shows that desired end-effector pose was achieved
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-1 -1.31387e-11-1.57726e-09 0.0999999
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-1.31386e-11 1 -7.46658e-08 0.2
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1.57726e-09-7.46658e-08-1 0.5
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0 0 0 1
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-1 -1.31387e-11-1.57726e-09 0.0999999
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-1.31386e-11 1 -7.46658e-08 0.2
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1.57726e-09-7.46658e-08-1 0.5
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0 0 0 1
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```
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Note that because this robot is redundant we don't have any control over the arm configuration apart from end-effector pose, ie. we can't control the elbow height.
@@ -135,29 +135,33 @@ robot.plot(qt.q, movie='panda1.gif')
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![Panda trajectory animation](https://github.com/petercorke/robotics-toolbox-python/raw/master/docs/figs/panda1.gif)
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which uses the default matplotlib backend.
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which uses the default matplotlib backend. Grey arrows show the joint axes and the colored frame shows the end-effector pose.
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Let's now load a URDF model of the same robotWe can instantiate our robot inside
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the 3d simulation environment. The kinematic representation is no longer
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Let's now load a URDF model of the same robot. The kinematic representation is no longer
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based on Denavit-Hartenberg parameters, it is now a rigid-body tree.
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```python
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robot = rtb.models.URDF.Panda() # load URDF version of the Panda
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print(robot) # display the model
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┌───┬──────────────┬─────────────┬──────────────┬─────────────────────────────────────────────┐
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│id │ link │ parent │ joint │ ETS │
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├───┼──────────────┼─────────────┼──────────────┼─────────────── 341A ─────────────────────────────┤
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│ 0 │ panda_link0 │ - │ │ │
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│ 1 │ panda_link1 │ panda_link0 │ panda_joint1 │ tz(0.333) * Rz(q0) │
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│ 2 │ panda_link2 │ panda_link1 │ panda_joint2 │ Rx(-90°) * Rz(q1) │
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│ 3 │ panda_link3 │ panda_link2 │ panda_joint3 │ ty(-0.316) * Rx(90°) * Rz(q2) │
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│ 4 │ panda_link4 │ panda_link3 │ panda_joint4 │ tx(0.0825) * Rx(90°) * Rz(q3) │
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│ 5 │ panda_link5 │ panda_link4 │ panda_joint5 │ tx(-0.0825) * ty(0.384) * Rx(-90°) * Rz(q4) │
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│ 6 │ panda_link6 │ panda_link5 │ panda_joint6 │ Rx(90°) * Rz(q5) │
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│ 7 │ panda_link7 │ panda_link6 │ panda_joint7 │ tx(0.088) * Rx(90°) * Rz(q6) │
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│ 8 │ @panda_link8 │ panda_link7 │ panda_joint8 │ tz(0.107) │
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└───┴──────────────┴─────────────┴──────────────┴─────────────────────────────────────────────┘
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┌───┬──────────────┬─────────────┬──────────────┬─────────────────────────────────────────────┐
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│id │ link │ parent │ joint │ ETS │
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├───┼──────────────┼─────────────┼──────────────┼─────────────────────────────────────────────┤
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│ 0 │ panda_link0 │ - │ │ │
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│ 1 │ panda_link1 │ panda_link0 │ panda_joint1 │ tz(0.333) * Rz(q0) │
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│ 2 │ panda_link2 │ panda_link1 │ panda_joint2 │ Rx(-90°) * Rz(q1) │
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│ 3 │ panda_link3 │ panda_link2 │ panda_joint3 │ ty(-0.316) * Rx(90°) * Rz(q2) │
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│ 4 │ panda_link4 │ panda_link3 │ panda_joint4 │ tx(0.0825) * Rx(90°) * Rz(q3) │
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│ 5 │ panda_link5 │ panda_link4 │ panda_joint5 │ tx(-0.0825) * ty(0.384) * Rx(-90°) * Rz(q4) │
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│ 6 │ panda_link6 │ panda_link5 │ panda_joint6 │ Rx(90°) * Rz(q5) │
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│ 7 │ panda_link7 │ panda_link6 │ panda_joint7 │ tx(0.088) * Rx(90°) * Rz(q6) │
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│ 8 │ @panda_link8 │ panda_link7 │ panda_joint8 │ tz(0.107) │
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└───┴──────────────┴─────────────┴──────────────┴─────────────────────────────────────────────┘
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```
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We can instantiate our robot inside a browser-based 3d-simulation environment.
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```python
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env = rtb.backend.Swift() # instantiate 3D browser-based visualizer
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env.launch() # activate it
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env.add(robot) # add robot to the 3D scene

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