Dynamic Parameter Identification

In order to identify the dynamic parameters of an articulated robot, the robot model is formulated as:

where is the joint torques, is a regressor matrix. The regressor matrix depends on the joint angles, velocities, and accelerations.

The Least-Square (SL) method is often applied in order to determine the inertial parameters. in general, it consists of the following several steps:

• Using the Newton-Euler formalism, generate a robot model that is linear in terms of the inertial parameters;
• reduce the inertial parameters set to a base set;
• determine the optimal trajectory parameters and optimize the excitation of the trajectories;
• estimate the link parameters using a standard least squares procedure.

In general, each link has 10 inertial parameters: its mass, the position vector of its center of gravity with respect to the base frame scaled by the link mass, 3 inertia moments, and 3 inertia products. Thus, an n-link manipulator has 10n dynamic parameters to be estimated. However, for the planar robot model, each link has only four parameters to be estimated: its mass, the position vector of its CoM with respect to the base frame, one inertia moment. Thus there are totally eight parameters for 2-link model. There are some hoses and wires connected to Sarcos, which apply external forces. However, this external forces change slightly during experiments. so we take them as a constant forces and additional parameters to be estimated. which are , , , .

The joint angles, , can be measured directly, but the angle velocity, , and the angle acceleration, , have to be numerically reconstructed. The reconstructing filter does not work in real time and thus it can be anti-causal, Therefore, a forward and reverse digital filtering can be used ². With the help of the inverse dynamic model, the joint torques and the ground reaction forces can then be predicted. Then we use these predicted values to fit the measurements, thus the dynamic parameters can then be determined by the following optimization problem:

where

and are computed joint torque, are computed groud reaction force, is the corresponding measurement vector, is the push size measurement, is the push location, is a weighted matrix of diag(1,1,1,1).

fitting data is e00120

Results: para1 = [51.2111 41.9894 0.1533 0.8000 -0.0622 0.7294 1.2563 1.7681 -0.0648 0 -8.1618 5.9660]
data are saved in soft.mat

There are large fitting errors when pushes are being applied. These errors may be caused by the arms and the knees movements, although they are almost fixed with high gain position controllers.