The code uses the Newton-Raphson root-finding algorithm to iteratively compute joint angles that achieve a desired end-effector position and orientation.
In robotics, DOF refers to the number of independent movements a robotic system can perform. A robotic arm with 6 DOF can move in three translational directions (X, Y, Z) and rotate about three axes (roll, pitch, yaw). This makes it capable of reaching any pose in 3D space.
A 6 DOF robotic manipulator, like the UR5 used in this project, can:
- Move forward and backward
- Move left and right
- Move up and down
- Rotate around its base
- Tilt its wrist up and down
- Rotate its wrist
Inverse Kinematics is the process of calculating the joint angles required for a robotic arm to reach a desired end-effector position and orientation.
Unlike forward kinematics, which computes the position of the end-effector given the joint angles, inverse kinematics solves the opposite problem: finding the necessary joint angles for a desired end-effector pose.
This project computes inverse kinematics for a UR5 robotic arm by:
- Defining the robot parameters (link lengths, offsets, and screw axes) in
kinematics.rs. - Using exponential mapping to calculate transformation matrices.
- Implementing numerical root-finding to iteratively solve for joint angles (
root_findingfunction).
Motion planners such as CHOMP, RRT, and Trajectory Optimization rely on inverse kinematics to generate feasible paths. For example:
- MoveIt! framework in ROS uses IK solvers to plan smooth motions.
- Trajectory optimization algorithms adjust robot paths while satisfying constraints.
In this project, a motion trajectory is planned by:
- Setting an initial pose and goal pose.
- Computing the desired transformation matrix.
- Iteratively solving for joint angles using root finding.
- Evaluating the final transformation matrix to verify correctness.
- Rust programming language
nalgebralibrary for matrix operations
cargo buildcargo run