Embedded Files
Dynamics
Dynamics
In the real time we do not have just six joint angle parameters. We have a bag parameter while making the robot do what it needed it to do. The parameters like motor torque, weight of the links, inertia adds more restriction in achieving the process. So, to study the forces and torques internally and the external loads acting on each joint require more powerful tools. The very first step in achieving the process is to calculate the equations of motion(EOM) for each joint using the Lagrange-Euler approach.
The first step in calculating the EOM is to calculate the Linear and Angular Jacoian. To calculate the Jacobians we need the position of COM of each link and Orientation of revolute joint axis with respect to the base frame. The Jacobian J is calcuated using the formula. Now it is necessary to calculate the kinetic energy and the potential energy. The first step is to derive the inertia matrix D(q) . Then finding the potential Energy equation. Now find the potential function by using differentiating with respect to the joint angle parameters g(q). Then it is necessary to find the Coriolis matrix C(q, qd)(qd is acronym of qdot denotes angular velocity and qdd is a acronym of q double dot denotes angular accelearation) which are the connection terms that ensures when we take the derivative of vector field that lives in the tangent space of the configuration manifold that the resulting derivatives stay within the same tangent space.
Z_i-1 is z-axis of the joint i-1
Pcom is the center of mass of link i
J_vi and J_wi are the linear and angular jacobian are obtained from the jacobian matrix J.
I_i is the inertia tensor calculated with respect to body frame.
Page updated
Google Sites
Report abuse