This repository contains code and documentation for controlling the Xarm6 robot. The project covers various aspects, including forward kinematics, inverse kinematics, numerical inverse kinematics, Jacobians, dynamics, and trajectory generation.

This code serves as a practical implementation of robotic kinematics and dynamics, focusing on the application of forward kinematics, inverse kinematics, workspace analysis, and Jacobian matrices. Specifically designed for the xarm6 machete robot, the code aims to provide a comprehensive tool for understanding and applying theoretical concepts from a robotics class to real-world scenarios.

Python environment with necessary libraries NumPy, Matplotlib, Pybullet.

The forward kinematics module is structured as a class, encapsulating various functions for frame transformations. Functions _0T1 to _5T6 calculate transformation matrices from one frame to another using Denavit-Hartenberg parameters. These matrices enable the determination of the robot's end effector position and orientation.

Functions _jointpos, _ori, and _endeff provide insights into the robot's configuration. _jointpos outputs the positions of each joint with respect to frame 0. _ori calculates the orientation of the end effector using Euler angles, and _endeff yields the transformation matrix for the end effector (Frame-6).

The _Jacobian function computes the Jacobian matrix, a crucial tool for understanding the robot's kinematics and aiding in tasks such as inverse kinematics and workspace analysis.

The Newton-Raphson algorithm is implemented for solving inverse kinematics. The iterative approach refines joint angles to achieve a desired end effector position.

The code leverages the Pybullet library for visualization, allowing users to observe the robot's motion and configuration in a simulated environment. The visualization component enhances the understanding of the robot's behavior and aids in debugging.

An additional feature incorporates the Jacobian matrix into the inverse kinematics solution. This enhancement improves the convergence speed and accuracy of joint angle adjustments.

The code includes the capability for inverse dynamics calculations, allowing for the determination of joint torques given external forces applied to the end effector.

A trajectory generation module employs cubic polynomials to plan smooth paths for the robotic arm. The implementation facilitates the robot's movement along predefined trajectories.

clone the following repo:

git clone https://github.com/bulletphysics/bullet3/tree/master

5.1 MODERN ROBOTICS MECHANICS, PLANNING, AND CONTROL. 5.2 Numerical Methods for Inverse Kinematics by Niels Joubert, UC Berkeley, CS184