This project also includes a complete symbolic and numerical analysis of the robot’s kinematics, Jacobian, and dynamics using MATLAB, complemented by motion profile generation with Python. The analytical approach provides deeper insight into robot behavior under realistic dynamic constraints.
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Kinematic Modeling (DH-Method):
- Symbolic generation of homogeneous transformation matrices.
- Computation of forward and inverse kinematics using algebraic and geometric methods.
- Workspace analysis based on over 200,000 evaluated configurations.
- Thermally induced length changes and required axis corrections.
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Jacobian and Force Analysis:
- Full derivation of the Jacobian matrix with respect to linear and angular velocity.
- Singular value decomposition (SVD) for singularity detection.
- Force and torque computation at each joint under given TCP loads.
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Lagrangian Dynamics:
- Symbolic derivation of Lagrange equations using kinetic and potential energy.
- Computation of:
- Mass matrix ( M(q) )
- Coriolis and centrifugal matrix ( C(q, \dot{q}) )
- Gravity vector ( G(q) )
- Numerical evaluation of (\boldsymbol{\tau}(t)) over time based on real motion profiles.
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MATLAB Scripts Include (only main files):
Auslegung_jacobi_iteractive_caipo_english.mAuslegung_lagrange_caipo_english.mAuslegung_Lagrange_iteractive_english.mAuslegung_RoboterAuslegung_english.m
- Motion Profile Generation:
- Implemented custom trajectory generation using jerk-limited motion profiles.
- Created time-continuous profiles for position, velocity, acceleration, and jerk.
- Exported profiles for use in dynamic torque evaluation in MATLAB.
- Complete URDF/XACRO structure of the SCARA robot.
- MoveIt 2 configuration for planning and collision avoidance.
- RViz visualization of robot structure and movements.
Manuel Caipo
Msc.Advanced Precision Engineering (APE)
Hochschule Furtwangen
Email: manuelcaipocc@outlook.com