Kinematics Algorithms

The geometry every arm program is built on. Chain transforms for forward kinematics, solve IK with damped least squares, and generate smooth trajectories through waypoints.

What you'll learn

• >Forward kinematics with homogeneous transforms
• >Numerical IK with damped least squares
• >Quintic trajectories through via points

Before you start

You should be comfortable with basic Python: variables, loops and functions. We'll introduce the robotics and the maths as you go. The first visit downloads the physics engine and Python, about 20 MB, and later visits load from your browser's cache.

Steps

1. 1Forward kinematicsChain one homogeneous transform per joint and link to get the gripper's full pose from the joint angles.Homogeneous transformsKinematic chainsRotation matricesOpen
2. 2Numerical inverse kinematicsIterate damped least-squares steps until the gripper reaches the target, or gets as close as the arm allows.Newton's methodDamped least squaresSingularitiesPro
3. 3Polynomial trajectoriesSolve for the quintic that meets position, velocity and acceleration at both ends, then chain quintics through waypoints.Boundary conditionsQuintic polynomialsVia pointsPro