纽约大学机器人基础matlab代码.zip

# Foundations-of-Robotics-NYU This repository includes the final project as part of the Foundations of Robotics course by Prof William Peng at NYU. The objective of the project is to explore and implement key robotics concepts, focusing on the kinematics, visualization and dynamics of David Bowen’s Plant Machete robot. The resemblance, especially in terms of the six degrees of freedom and the physical design of the links, guided our decision to model our project on the Ufactory Xarm 6. We implemented our project, utilizing MATLAB as our primary tool for executing the tasks of the project, which included the development of forward kinematics, inverse kinematics, pose visualization, application of the Jacobian method in both inverse kinematics and inverse dynamics, and workspace visualization. ## Visualization: Robotic Systems Toolbox is used in this code for visualizing the robot poses. The 3D model of the robot is stored in the Xarm6_description folder, which also contains other information such as the location and types of joints of the robot. The robot model is imported to MATLAB using the importrobot() function with the path to the .xacro file ( "Xarm6_description/urdf/Xarm6.xacro") as the input. DataFormat parameter to the importrobot function is set to “row” for easier handling of the visualization code. The imported model, stored in the variable ‘m6r’, is then passed as a parameter to the show() function along with the joint angles vector for displaying the robot pose. <img width="515" alt="image" src="https://github.com/Santoshsrini/Foundations-of-Robotics-NYU/assets/28926309/61779091-1101-4249-a136-77720db2546e"> ## Forward Kinematics: The fwd_kin function computes the positions of the origins of link frames and the end-effector frame for given joint angles. Also, it produces a visual representation of the corresponding pose of the robot. Input: 1*6 array of joint angles Output: Position of joints (px, py,pz) and end effector position <img width="529" alt="image" src="https://github.com/Santoshsrini/Foundations-of-Robotics-NYU/assets/28926309/02200acb-6ef4-4334-b4ec-f4cc865711f4"> ## Inverse Kinematics: Inverse kinematics calculates the joint parameters needed to achieve a specific position and orientation of the end effector. The joint parameters are computed by solving equations that are obtained by equating the forward kinematics model of the manipulator to the desired end effector position and orientation using fsolve optimisation. Input: A 1x6 array containing end effector position in cm and moving XYZ Euler angles in radians Output: Joint angles if solution is found, else the message “Given position and orientation is not attainable”. The corresponding robot pose is also displayed if a solution is found. <img width="499" alt="image" src="https://github.com/Santoshsrini/Foundations-of-Robotics-NYU/assets/28926309/78565ae5-67f6-49dd-bd50-bfa9e19a8ea5"> ## Inverse Kinematics with Jacobian: The joint_vel function calculates the joint angular velocities (qd) of a robotic arm for a given end effector position (pos) and velocity (vel). It first obtains the Jacobian matrix as a function using Jacob(), and then determines the joint angles corresponding to the specified end effector position using inv_kin(pos). If the position is reachable and not at a singular point (where the Jacobian determinant is not zero), the function computes the joint velocities by inverting the Jacobian and multiplying it with the end effector velocities (vel). If the position is unreachable or a singular point, the function displays an appropriate message and exits. Input: 1*6 array containing end effector position and XYZ Moving Euler angles and 1*6 array containing end effector linear and angular velocity Output: 1*6 array containing Joint angular velocities <img width="505" alt="image" src="https://github.com/Santoshsrini/Foundations-of-Robotics-NYU/assets/28926309/483a4404-2af6-4b5d-8a16-bcca565fb7b8"> ## Inverse Dynamics with Jacobian: The function joint_torques computes the joint torques (F) for a given end effector position , orientation and external forces/moments acting on it. It first derives the joint angles for the specified position and orientation using inv_kin(pos) and then obtains the Jacobian matrix using the Jacob() function. The function checks for reachability of the position and singularity (where the Jacobian determinant is zero). If the position is reachable and non-singular, it calculates the joint torques by multiplying the transpose of the Jacobian with the negative of the external forces/moments. Input: 1*6 array containing end effector position and XYZ Moving Euler angles and 1*6 array containing force and moment at the end effector Output: 1*6 array containing Joint Torques <img width="518" alt="image" src="https://github.com/Santoshsrini/Foundations-of-Robotics-NYU/assets/28926309/07113e17-9a51-48bd-bf28-6b56fcab33e5">