Kinematics / Dynamics

Code developed while doing course assignments for the kinematics and dynamics of different robotic systems.

Contents:

1. FK/IK for a 5-DOF manipulator

   • For forward kinematics, all the joint positions and transformation matrices are computed using DH method.
   • For inverse kinematics, the code uses kinematic decoupling and has checked joint limits, feasibility, and considered other edge cases.
   • Call functions calculateFK and calculateIK to compute the results.

2. 2D pendulum dynamics

   • The dynamics.m uses the Euler-Lagrange method to derive the closed-form equation of motion for the pendulum model. The symbolic expression has been copied to the solution.m script. Run solution.m directly to solve the ODE and plot for joint variable values w.r.t. time (assume torque = 0).
   • The other type of dynamics problem it solves is that when the functions of joint variables w.r.t. time is known. In this case, run torque.m to compute the desired torques to along this trajectory.
   • The code solves the dynamics problem of system DOF = 2, but it is easy to be revised for solving higher-order pendulum dynamics models. However, some matrix manipulation may be needed beforehand to simplify the computation since the differentiation in MATLAB takes a lot more time as the number of symbolic variables grow.

3. Velocity kinematics for a mobile manipulator

   • The mobile manipulator is a 3-joint manipulator with a mobile base (differential drive). The jacobian.m code stores the Jacobian matrix of the system, which is used to transform the end-effector velocity to each joint's velocity. The main.m simulates the motion and animate.m creates the animation.
   • There are 4 types of tests you can run in main.m. Two of them are shown in the animation below. In these two tests, the end-effector draws a square shape. The code computes and executes the velocity of each joint using the functions mentioned above to achieve the desired motion.
   • Test 1 (mobile base unlocked)

   

   • Test 2 (mobile base locked)