Basic Pick and Place

The Pick-Place Pipeline

1. Perceive object pose
2. Plan approach trajectory
3. Execute grasp
4. Move to goal
5. Release object

Spatial Algebra

Rotation Representations

• Euler angles
• Quaternions
• Axis-angle

Homogeneous Transforms

\[T = \begin{bmatrix} R & p \\ 0 & 1 \end{bmatrix}\]

Forward Kinematics

Using Drake's MultibodyPlant:

plant = builder.AddSystem(MultibodyPlant(time_step))
parser = Parser(plant)
parser.AddModelFromFile("robot.sdf")
plant.Finalize()

context = plant.CreateDefaultContext()
X_WB = plant.CalcForwardKinematics(context)

Inverse Kinematics

Numerical IK with Drake

def solve_ik(plant, context, X_WG):
    ik = InverseKinematics(plant, context)
    ik.AddOrientationConstraint(...)
    ik.AddPositionConstraint(...)
    result = Solve(ik.prog())
    return result.GetSolution()

Grasp Selection

• Predefined grasp poses
• Grasp quality metrics
• Grasp planning algorithms

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