Key Engineering Takeaways
- •Analytical IK is deterministic and computes all possible solutions in microseconds; numerical IK works on arbitrary kinematic topologies.
- •A 6-DOF arm has closed-form IK if three consecutive joint axes intersect at a single point (Spherical Wrist).
- •Damped Least Squares (DLS) prevents joint velocity explosion near singular configurations: J* = Jᵀ(JJᵀ + λ²I)⁻¹.
Prerequisites
- • Forward Kinematics
- • Jacobian matrix basics
Analytical Closed-Form vs Numerical Iterative IK
While Forward Kinematics always produces a single unique end-effector pose, Inverse Kinematics (IK) is non-linear, non-unique, and may have zero solutions (target outside reachable workspace), multiple solutions (elbow up vs elbow down), or infinite solutions (kinematic redundancy).
Tags:#Inverse Kinematics#IK#Pieper Criterion#Jacobian#DLS#Optimization