Robot Kinematics and Control
Forward/inverse kinematics, PID and trajectory control.
Taught by Sristi Maharjan · Robotics Engineer
What you'll learn
- Represent orientation and pose with rotation matrices, quaternions and homogeneous transforms in NumPy
- Derive and implement forward kinematics for a serial arm from Denavit-Hartenberg parameters
- Solve inverse kinematics analytically for a planar arm and numerically with damped least squares
- Compute the manipulator Jacobian and use it for velocity mapping, force mapping and singularity detection
- Implement, simulate and tune a discrete PID joint controller with anti-windup and feedforward
- Generate cubic, quintic and trapezoidal trajectories and execute them through a joint trajectory interface
About this course
This advanced course covers the mathematics that makes robot arms and legs move where you want them, implemented in Python with NumPy and SciPy so every idea becomes working code. You will represent poses with rotation matrices, quaternions and homogeneous transforms, derive forward kinematics from Denavit-Hartenberg parameters, solve inverse kinematics both analytically and with Jacobian-based numerical methods, and use the Jacobian to reason about velocities, forces and singularities. The control half builds a discrete PID controller for a simulated joint, tunes it methodically with anti-windup and feedforward, and generates smooth cubic, quintic and trapezoidal trajectories that a real controller can track. It is written for engineering students, graduates and developers who are comfortable with linear algebra, calculus and Python and want the university-core robotics content that interviews and research positions expect. Each lesson ends with exercises that extend the code, and the final project moves a simulated arm along a planned Cartesian path.
Course content
6 lessons- 1Rigid-Body Transforms: Rotations, Poses and FramesRotation matrices, Euler angles, quaternions and homogeneous transforms, composed correctly in NumPy and SciPy.Preview
- 2Forward Kinematics with Denavit-Hartenberg ParametersAssign DH frames, derive the four parameters per joint, and compute the end-effector pose of a serial arm.
- 3Inverse Kinematics: Analytic and NumericalSolve joint angles for a target pose in closed form for a planar arm and numerically with damped least squares.
- 4Jacobians, Velocities and SingularitiesBuild the manipulator Jacobian, map joint rates to tool velocity and forces, and detect and avoid singular poses.
- 5PID Joint Control and TuningImplement a discrete PID controller on a simulated joint, then tune it with anti-windup and feedforward.
- 6Trajectory Generation and ExecutionGenerate smooth cubic, quintic and trapezoidal profiles, plan in joint or Cartesian space, and execute them.