russtedrake PRO
Roboticist at MIT and TRI
Basic Pick and Place
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(or later at https://slides.com/russtedrake/fall23-lec05)
MIT 6.4210/2: Robotic Manipulation
Fall 2023, Lecture 5
(part 3)
Basic Pick and Place
Step 1: Kinematic Frames / Spatial Algebra
Step 2: Gripper Frame Plan "Sketch"
Step 3: Forward kinematics of the iiwa + WSG
Step 4: Differential Inverse Kinematics
Kinematic Jacobian: \( {}^WV^G = J^{G}(q) v \)
\( v = [J^{G}(q)]^{+} {}^WV^G \)
spatial velocity
generalized velocity
Kinematics
- Forward kinematics: joint positions \(\Rightarrow\) pose
- Inverse kinematics*: pose \(\Rightarrow\) joint positions
-
Differential kinematics:
joint positions, velocities \(\Rightarrow\) spatial velocity
-
Differential inverse kinematics:
spatial velocity, joint positions \(\Rightarrow\) joint velocities
q \Rightarrow X^B
X^B \Rightarrow q
q, v \Rightarrow V^B
V^B, q \Rightarrow v
Our first Jacobian pseudo-inverse controller
\( v = [J^{G}(q)]^{+}\,{}^WV^G \)
prog = MathematicalProgram()
x = prog.NewContinuousVariables(2)
prog.AddConstraint(x[0] + x[1] == 1)
prog.AddConstraint(x[0] <= x[1])
prog.AddCost(x[0] ** 2 + x[1] ** 2)
result = Solve(prog)
Lecture 5: Basic pick and place (part 3)
By russtedrake
Lecture 5: Basic pick and place (part 3)
MIT Robotic Manipulation Fall 2023 http://manipulation.csail.mit.edu
