Robotics in 3D with Python

About: A first course in 3D robotics. The material teaches fundamentals of robotics in this order: kinematics (homogenous transformation, Euler angles, rotation matrices, quaternions, forward and inverse kinematics), differential kinematics (velocity and jacobian), dynamics (Euler-Lagrange equations, Recursive Newton-Euler Algorithm, TMT method), and control (trajectory generation, trajectory tracking). The methods are demonstrated on a custom created planar 3R manipulator, the UR5 manipulator, and the Unitree A1 quadruped robot in simulation. The course emphasizes theory by deriving necessary formulae and algorithms and validating them by comparing with MuJoCo (python). For example, we derive a numerical method of computing the Jacobian and then verify with mj_Jac availabe in MuJoCo. Similarly, we use Recursive Newton Euler Method Algorithm (RNEA) to derive the equations of motion using the forward kinematic recursion and backward force/torque recursion and verify the same with mj_fullM and data.qfrc_bias from MuJoCo.

Click the links for YouTube playlists: Robotics 3D and MuJoCo 3.2.6 using Python.


NEW (12/12/25): All 10 Homeworks are now available.
I recommend installing Visual Studio Code IDE for python.

• If you are looking for 2D Robotics with MATLAB see this link: tiny.cc/robotics.
• If you are looking for 2D Robotics with Python and MuJoCo see this link: tiny.cc/roboticspy.
• If you are looking for 2D Robotics with Python and Coppelia see this link: tiny.cc/robotics24.

#	Topic	Youtube	Notes	Code
	Introduction
Lec0	Syllabus	Video	None	None
Lec01	Introduction to Python	Video	None	Code
	Kinematics
Lec02	Homogenous Transformation	Video	PDF	None
Lec03a	Euler Angles (123 or xyz convention)	Video	PDF	Code
Lec03b	Rotations in 3D dont commute and in 2D they commute	Video	see above	None
Lec03c	Gimbal Lock	Video	see above	None
Lec04	Relation between Quaternions, Axis-Angle, Rotation, Euler Angles	Video	PDF	None
Lec05a	Planar 3R, Forward Kinematics, Theory	Video	see above	None
Lec05b	Planar 3R, Forward Kinematics \& Reachable Space, Python Code	Video	PDF	None
MJC	Planar manipulator, Modeling (1 of 2)	Video	see above	Code
MJC	Planar manipulator, Forward Kinematics (2 of 2)	Video	see above	None
MJC	UR5, Interpreting the XML file (1 of 3)	Video	see above	Code
MJC	UR5, Converting UR5 XML to Homogenous Transformations for Forward Kinematics (2 of 3)	Video	see above	None
MJC	UR5, Forward Kinematics in MuJoCo and verify with homogenous transformation (3 of 3)	Video	see above	None
Lec06a	Planar 3R, Inverse Kinematics, Theory and Algebraic Solution	Video	PDF	Code
Lec06b	Non-Planar 3R manipulator, Inverse Kinematics, Geometric Solution	Video	see above	None
Lec06c	Planar 3R, Inverse Kinematics, Numerical Solution	Video	see above	None
MjC	UR5, Inverse Kinematics for a single pose in MuJoCo (1 of 2)	Video	see above	Code
MJC	UR5, Inverse Kinematics for a trajectory in MuJoCo (2 of 2)	Video	see above	None
	Differential Kinematics
Lec07a	Introduction to Linear/Angular Velocity of a Floating Body	Video	PDF	Code
Lec07b	Relation between angular velocity and Euler rates Floating Body	Video	see above	None
Lec07c	Relation between angular velocity and quaternion Floating Body	Video	see above	None
Lec08	Linear and Angular Velocity Recursion for Manipulators	Video	PDF	None
MJC	Velocity Propagation formula, planar 3R (1 of 2)	Video	see above	Code
MJC	Velocity Propagation formula, UR5 (2 of 2)	Video	see above	Code
Lec09a	Introduction to Jacobian	Video	PDF	None
Lec09b	Jacobian calculation for planar 3R manipulator	Video	see above	None
Lec09c	Jacobian for static forces, planar 3R manipulator	Video	see above	None
MJC	Jacobian, planar 3R (1 of 2)	Video	see above	Code
MJC	Jacobian, UR5 (2 of 2)	Video	see above	Code
	Dynamics
Lec10a	Dynamics equations for free-floating body and intro to derivation	Video	PDF	Code
Lec10b	Euler-Lagrange Method with a simple example	Video	see above	None
Lec10c	Euler-Lagrange Method with a planar 3-link manipulator	Video	see above	None
Lec10d	Recursive Newton Euler Algorithm, RNEA	Video	see above	None
Lec10e	Recursive Newton Euler Algorithm for a planar 3R manipulator	Video	see above	None
MJC	Recursive Newton Euler Algorithm (RNEA), Planar 3R manipulator	Video	see above	Code
MJC	Recursive Newton Euler Algorithm (RNEA), UR5 manipulator	Video	see above	Code
MJC	TMT Method to compute Mass Matrix, UR5 manipulator	Video	see above	None
	Control
Lec11a	Trajectory generation using Polynomials and Cubic Splines	Video	PDF	Code
MJC	Trajectory Generation in Joint Space for UR5 manipulator	Video	see above	Code
MJC	Trajectory Generation in Task Space for planar 3R manipulator	Video	see above	Code
Lec11b	Compare linear interpolation using Euler angle/rotation/quaternions	Video	see above	None
MJC	Compare linear interpolation using Euler Angles / Rotation Matrices / Quaternions	Video	see above	Code
Lec11c	Trajectory generation for orientation using LERP and SLERP	Video	see above	None
MJC	Trajectory generation for orientation using LERP and SLERP	Video	see above	Code
Lec12a	Tracking control, Inverse Dynamics and Feedforward/Feedback Control	Video	PDF	None
MJC	Trajectory Tracking using Feedforward/Feedback on UR5	Video	see above	Code
Lec12b	Lyapunov function and La Salles Invariance	Video	see above	None
Lec12c	Task Space or Cartesian Space control	Video	see above	Code
Lec12d	Force/Impedance/Hybrid-Force Position Control	Video	see above	Code
Lec13a	Introduction to the Unitree A1 quadruped	Video	PDF	None
Lec13b	Unitree A1 quadruped, Programming the state machine	Video	see above	Code
Lec13c	Unitree A1 quadruped, Programming trajectory generation	Video	see above	None
Lec13d	Unitree A1 quadruped, Programming tracking control for joints	Video	see above	None
Lec13e	Unitree A1 quadruped, Programming tracking control for body	Video	see above	None
	Others
Lec14a	Setting up camera and using OpenCV	Video	PDF	Code
Lec14b	Setting up fake gripping using a touch sensor	Video	see above	Code
Lec14c	Setting up rangefinder, adding noise and filtering	Video	see above	Code
Lec15	Motion Planning, Local planners	Video	PDF	Code
Lec16	Optimization: Inverse Kinematics and Motion Planning using MPC	Video	PDF	Code