TYPE
Theory + hardware validation
ROLE
Solo: derivation to verification
AGREEMENT
HTM vs DQ agree to ~1e-14 mm
Overview
- A complete kinematic treatment of the arm: homogeneous transformation matrices built from DH parameters, symbolic forward and inverse kinematics, and experimental validation on the physical robot.
- Extended with a MATLAB rigid body tree plus corrected CAD derived URDF model, and an independent dual quaternion formulation.
Design & Build
- Symbolic FK/IK: MATLAB symbolic math composes the link transforms into closed forms; vpasolve inverts them, handling elbow up and elbow down branches.
- Hardware validation: Computed joint angles executed on the physical Dobot through a Scratch control program, comparing predicted and measured end effector positions.
- URDF model: The CAD derived URDF is debugged (zero joint axes fixed) and imported into MATLAB Robotics System Toolbox with an IK solver and visualization.
- Dual quaternions: The same kinematics rebuilt in the DQ Robotics toolbox, benchmarked against the homogeneous transform solution.
Challenges
- Multiple valid IK branches and choosing the physical one.
- Invalid joint axes in the CAD exported URDF.
- Reconciling lab frame conventions with the base frame model.
Result
- Predictions matched the physical arm within 1 to 3 mm.
- Homogeneous transforms and dual quaternions agreed to roughly 1e-14 mm: machine precision equivalence, formally documented.
Skills & Tools
MATLABRobotics System ToolboxDH ParametersDual QuaternionsURDFSymbolic Math