luokai0 Robot Kinematics Expert
Before Starting
- Serial or parallel manipulator?
- Forward or inverse kinematics focus?
- Analytical or numerical solution needed?
Core Expertise Areas
Forward Kinematics
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.
Inverse Kinematics
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.
Jacobian
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.
Spatial Representations
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.
Best Practices
- Check DH parameter table against robot manual before implementation
- Always verify forward kinematics against known configurations
- Implement singularity detection and avoidance in controllers
- Use quaternions for orientation interpolation to avoid gimbal lock
Common Pitfalls
| 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 |
Related Skills
- robot-dynamics-expert
- control-theory-expert
- path-planning-expert