Robotic Manipulator & Arm Kinematics Roadmap
Master 6-DOF industrial robot arms: DH parameters, forward/inverse kinematics, MoveIt 2, and trajectory generation.
Learn the core robotics mathematics and control systems required to build, simulate, and control multi-axis robotic arms from desktop servos to industrial 6-axis articulated manipulators.
Roadmap Curriculum & Milestones
Complete each sequential phase to build production-grade robotics competencies.
Phase 1: Spatial Mathematics & Forward Kinematics
Represent 3D poses, rotations (SO(3)), transformations (SE(3)), and standard Denavit-Hartenberg conventions.
Rotations, Euler Angles, Quaternions & Homogeneous Matrices
Understand 3D coordinate frames, Euler angle singularities (Gimbal lock), unit quaternions, and 4x4 transformation matrices.
- SO(3) & SE(3) Groups
- Quaternion Algebra & SLERP
- Transformation Composition
- Frame Inversion
- Interactive 3D Coordinate Frame Visualizer in Python/OpenGL
Denavit-Hartenberg (DH) Convention & FK Solver
Formulate Standard and Modified DH parameter tables for 3-DOF, 4-DOF, and 6-DOF robotic arms to compute end-effector position and orientation.
- DH Table Formulation (a, alpha, d, theta)
- Forward Kinematics Matrix Chain Rule
- End-Effector Pose Computation
- 6-DOF Puma 560 / UR5 Forward Kinematics solver in C++
Phase 2: Inverse Kinematics & Velocity Kinematics (Jacobian)
Solve inverse kinematics using analytical algebraic methods and iterative numerical optimization algorithms.
Analytical & Numerical Inverse Kinematics (IK)
Solve closed-form IK for robots with spherical wrists (Pieper criterion) and numerical IK using Damped Least Squares (Levenberg-Marquardt).
- Geometric IK Decoupling
- Spherical Wrist Decoupling
- Jacobian Pseudoinverse (Moore-Penrose)
- Singularity Handling & Damping
- Real-time 6-axis IK solver with singularity avoidance
Manipulator Jacobian, Statics & Computed Torque Control
Relate joint velocities to Cartesian end-effector velocities, compute manipulability ellipsoids, and model joint torques with Euler-Lagrange equations.
- Geometric Jacobian
- Manipulability Measure
- Euler-Lagrange Equations of Motion
- Gravity & Coriolis Compensation
- Gravity-compensated computed-torque controller in simulation
Phase 3: Motion Planning with MoveIt 2 & ROS 2 Control
Integrate collision detection, sampling-based path planners (OMPL/RRTConnect), and hardware servo interfaces.
MoveIt 2 Trajectory Planning & Collision Avoidance
Set up MoveIt 2 configuration packages, define planning groups, and execute collision-free pick-and-place trajectories.
- MoveIt 2 Setup Assistant
- OMPL (RRT*, PRM*) Planners
- OctoMap 3D Collision Checking
- ros2_control Hardware Interface
- Autonomous 6-DOF Pick-and-Place pipeline with 3D Depth Camera
Ready to begin Phase 1?
Dive into our free hands-on tutorials and build your first physical prototype.