Analysis of Least Norm Solution Error

In this section selected quantitative aspects of the recorded ADLs were used to establish aspects of human motion control. Analyzing the movement of the distal joints relative to the least norm solution provides insight into the motivations behind human movement. To establish joints of interest the joints with the highest error were analyzed in detail. Data from the ten control subjects were used to find the error associated with the least norm solution. The least norm solution was used to find joints of potential interest for analysis and discussion. Table 24 and Table 25 show the RMS error on subject and task basis respectively. The error of the least norm solution is used as a baseline of

comparison for the more complicated methods.

Table 24: Right arm RMS subject error for LN solution (degrees)

Subject 1 2 3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 Avg. S.D. C01 15 6 7 4 8 14 17 10 24 18 5 10 7 10 11 6 C02 17 6 4 7 11 10 9 11 16 19 7 15 15 12 11 5 C03 15 4 5 5 14 10 12 11 17 18 9 11 12 9 11 4 C04 19 5 7 8 16 16 14 14 21 16 14 16 15 9 13 5 C05 21 6 6 7 13 14 18 14 24 16 11 13 11 8 13 5 C06 14 4 5 8 7 11 11 6 14 21 7 13 8 12 10 5 C07 12 3 5 4 7 11 10 13 22 18 7 11 7 10 10 5 C08 18 7 4 4 16 10 19 12 23 17 8 15 13 6 12 6 C09 12 4 9 6 8 9 12 8 18 10 10 10 10 7 9 3 C10 17 4 7 7 6 9 18 10 22 27 15 15 11 8 13 7 Avg. 16 5 6 6 11 11 14 11 20 18 9 13 11 9 11 S.D. 3 1 1 1 4 2 4 3 4 4 3 2 3 2

The joints for the dominant arm with the highest RMS error are joints D9, followed by joints D10, 1, and D7, which represent upper arm rotation, elbow flexion, torso flexion, and upper arm flexion respectively. The brushing hair and opening a door ADLs had the highest error for the tasks, and subjects C04, C05 and C10 had the highest errors for subjects.

Table 25: Right arm RMS task error for LN solution (degrees) Task 1 2 3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 Avg. S.D. Brush 25 6 7 6 14 13 14 16 26 25 10 15 15 13 15 7 Drink 10 3 6 4 7 8 13 7 18 7 6 5 5 6 8 4 Eat 8 4 4 4 7 7 12 6 11 9 5 9 9 6 7 2 Lift 17 5 6 6 13 11 16 10 22 18 9 9 10 7 11 5 Open 16 5 8 8 10 15 13 10 19 17 13 18 11 7 12 4 Avg. 15 5 6 5 10 11 14 10 19 15 9 11 10 8 11 S.D. 7 1 1 2 3 3 2 4 6 7 3 5 4 3

It is interesting to note that there is a greater variation in error between joints than between subjects or tasks, and a greater variation between tasks than subjects. In Sub- sections 6.1.1 through 6.1.5 joints with high error are investigated in detail.

6.1.1 Brushing Hair

Some movement of the torso was typically involved when picking up and putting down the brush, however, the majority of the movement for this task comes from the upper arm and forearm. In the least norm solution the proximal joints, torso flexion in particular, have an increased movement relative to the recorded joint angles, as shown in Figure 30.

Figure 30: Upper arm rotation (left) and torso flexion (right) joint angles (rad) (top) and rotational velocity (rad/sample) (bottom) relative to time (sample 20Hz) for

The least norm solution results in greater movement of the torso, joint 1, and decreased movement of the shoulder, joint D9. The velocity profile of the least norm solution was similar to the recorded data; this shows the areas where the ability of the joint to perform the task movement is highly correlated with the recorded motion. There is also a

considerable amount of noise in the recorded joint velocity, suggesting that additional filtering may be necessary if using joint velocity in a control algorithm.

6.1.2 Drinking From a Cup

In this task the cup must be raised to the mouth and be properly oriented. The cup must remain vertical while it was being raised to the mouth, and carefully controlled as the user drank (although in our recording the cup was empty so the control was potentially not as strict). Since the relative position of the mouth to the hand is independent of torso orientation there was, very little movement of the torso, as shown in Figure 31.

Figure 31: Upper arm rotation (left) and torso flexion (right) joint angles (top) and rotational velocity (bottom), recorded data and least norm solution, drinking task,

The difference between the least norm solution and the recorded data were even more evident in this task. The least norm solution had a large amount of movement in torso flexion, and very little movement in upper arm rotation.

6.1.3 Eating With a Knife and Fork

The eating task was performed from a seated position and was a bilateral task. It requires dexterous movement of the wrist for the positioning of the utensils. For this task joints D10 and D12, elbow flexion and forearm pronation, were investigated. The elbow flexion angle had a high angular velocity when the subject performed a cutting motion. The wrist has a few movements throughout the trial, an initial orientation, an orientation for cutting, and a peak where the food is brought to the mouth. The ability of the least norm solution to predict the proper motion can be seen in that the paths are similar, but there appears to be a difference in the magnitude of movement. This suggests that the weighted least norm solution may be sufficient to predict the motion of this task, at least for this subject.

Figure 32: Elbow flexion (left) and forearm pronation (right) joint angles (rad) (top) and rotational velocity (rad/sample) (bottom) relative to time (sample 20Hz),

6.1.4 Lifting a Laundry Basket

This task requires a large amount of movement in the torso, as well as the ability to lift a load. The task is nearly symmetric for the arms, so we see similar joint profiles in the right and left joints for the control subjects. The joints 1 and D7 representing flexion of the torso and upper arm respectively, were investigated for this task. In this case we see that the least norm solution is actually predicting a smaller range of motion in the torso and the upper arm than in the recorded data. This is likely due to the position of the joints at the start of the task, from a comfortable standing position the instantaneous velocity produce by torso flexion is primarily forward, where the desired path is for the hands to move downward towards the basket. The change of pose of the subject from one that is comfortable for normal standing, to one that better facilitates the performance of the tasks is likely the reason the least norm solution performs poorly for this task.

Figure 33: Torso flexion (left) and upper arm flexion (right) joint angles (rad) (top) and rotational velocity (rad/sample) (bottom) relative to time (sample 20Hz),

6.1.5 Opening a Door

This task requires dexterous manipulation at a location that is often on the edge of the workspace. The natural inclination is to stand sufficiently far away from the door to permit its opening without moving backward. This requires movement of the torso and upper arm to bring the hand to the knob, and the motion of the wrist and forearm to turn the knob and open the door. Joints 1 and D9, torso flexion and upper arm rotation, were investigated for this task. Similarly to brushing hair and drinking from a cup, there was increased movement of the torso for the least norm solution, and decreased movement of the upper arm.

Figure 34: Torso flexion (left) and upper arm rotation (right) joint angles (rad) (top) and rotational velocity (rad/sample) (bottom) relative to time (sample 20Hz),

recorded data and least norm solution, opening task, subject C02

From these analyses it is clear that the least norm solution is a poor predictor of human pose, but it does provide insight into the relation between the task and the joint

was filtered, it is clear that a noise remains in the joint angle data and that additional filtering may be required if the angular velocity is to be used in control algorithms.