Force/torque predictions and lab test data

The goal is to use measured data from an ATI six-axis force/torque sensor to verify predicted interaction forces and torques. Recall the equations of motion governing these take the form:

q represents rigid joint angles and q represents flexible base motion. I am particularly interested in the inertia effects B_F and B_t0, but the force/torque sensor picks up all of the effects. Thus, in order to better isolate the interactions due to the rigid robot (which are the effects that are directly controllable), I braced the flexible beam as shown in Figure 1. Input signals were sent to the 3 DOF rigid robot similar to the motion expected during active inertial damping.

Figure 1

Braced Testbed Macromanipulator

The first part of this work involved actuating each joint independently, with sinusoidal inputs at 1 Hz, slightly lower than the first natural frequency of the flexible link. It was expected this would create dominant inertial forces since:

The model for the inertia forces

An example of predicted and measured forces due to joint 1's motion, along with predicted nonlinear rigid effects (N_F), are shown in figure 2 and torques in figure 3.

Figure 2

Comparison of predicted and measured interaction forces

Figure 3

Comparison of predicted and measured interaction torques

From these tests I made some updates to the robot's inertia properties and compared predicted inertial and measured forces and torques corresponding to each term in the B_F and B_t0 matrices with inputs at 1 and 2 Hz. To quantify the comparisons I calculated the correlation factor for each fit, with an average correlation of .975 (forces) and .955 (torques). This really just verified what we already knew: good inertial forces and torques can be created in limited degrees of freedom.

The next part involved extending this to multiple degrees of freedom. Figure 4 shows predicted and measured interaction forces due to joints 1, 2, and 3 actuating simultaneous (at 1, 1.5, 2 Hz, respectively). In configurations where we have predicted good inertial forces, the results are clean. Unfortunately, in other configurations the relationship becomes more complicated and the ability of the scheme to accurately predict the interaction forces by considering the inertial effects alone does not work well (Figure 5) and we begin to see higher frequency phenomena. In certain configurations, nonlinear effects can become significant compared to the inertial effects (next section).

Figure 4

Measured interaction forces and predictions in 3 DOF

Figure 5

Measured interaction torques and predictions in 3 DOF