Expert-level robot kinematics covering forward and inverse kinematics, Denavit-Hartenberg parameters, workspace analysis, singularities, and Jacobian-based methods.
DH parameters: four parameters per joint define frame transformations. Homogeneous transformation: 4x4 matrix combining rotation and translation. Frame assignment: DH convention assigns frames to each link systematically. End-effector pose: product of joint transformation matrices. Modified DH: Craig convention places frame at proximal joint.
Analytical IK: closed-form solution, fast, handles all configurations. Numerical IK: iterative Jacobian-based methods, general but may not converge. Multiple solutions: most robots have multiple IK solutions for same end-effector pose. Singularities: configurations where Jacobian loses rank, infinite IK solutions. Workspace: reachable and dexterous workspace depend on link lengths and joint limits.
Geometric Jacobian: maps joint velocities to end-effector velocities. Analytical Jacobian: partial derivatives of forward kinematics with respect to joint angles. Jacobian transpose: simple inverse kinematics controller, no matrix inversion. Pseudoinverse: minimum norm solution for redundant robots. Damped least squares: avoids singularity issues in numerical IK.
Rotation matrices: 3x3 orthogonal, no singularity but 9 parameters for 3 DOF. Euler angles: minimal representation, suffer from gimbal lock. Quaternions: 4 parameters, no singularity, efficient for interpolation. Axis-angle: intuitive, axis unit vector plus rotation angle.
| Pitfall | Fix |
|---|---|
| Wrong DH convention | Clarify standard vs modified DH before implementation |
| Ignoring joint limits in IK | Filter solutions violating joint limits |
| Euler angle gimbal lock | Switch to quaternions or rotation matrices |
| Jacobian singularity causing instability | Add damping or singularity avoidance |