THINKING AND SELF CONCIOUSNESS?
5.1 INT RODUCTION
9.1: Tracking a Guarded Move
177
x y z Z
YZ 3 XZ Path that results
from down and back command
Figure 9.2: The ngertip on the PHANToM , represented by the sphere, is commanded to move down and back, with a single command, using position control. The constraint surfaces are labeled as (Z), (YZ), (XZ) and 3. The command takes the ngertip from 3 to Z to YZ to 3.
alternatives as possible decisions, it will make arbitrary decisions against what is essentially noise. An experiment discussed in the next section illustrates this issue.
stick-178
Chapter 9: TasksRobot Environment Fe Fc
-+ Ki Fnet
1/s +
K(1+λ s)
-Xc
X
Figure 9.3: Integral endpoint force controller with position feedback.
slip as it moved across the at surface. This had to be explicitly accounted for in the feature model. Sticking was modeled by allowing transition from (MC, Z, M) to a (S, 3, F). Then slipping was modeled by adding a connection from (S, 3, F) back to (MC,Z,M) possibly through an impact mode, thus the stick-slip that occurs as the ngertip moves along the surface is modeled a multiple transitions between these two .
Although this works reasonably well, a better approach was to change the underlying controller. An integral based endpoint force controller was added in parallel to the position controller (Figure 9.3). With this controller, the desired force input can be used as the basic command. In free space, this command becomes a constant velocity command. In contact, the controller will maintain a constant force against the constraints if the constraints support the desired force. A constant velocity will result from the forces that are not supported by the constraints. The controller acts like a generalized damper with a very narrow velocity error cone. All the remaining experimentsgiven in this section and in the maze were performed with this controller.
With this controller, the desired action becomes the command (100,-100,200) where the command is a vector desired force to achieve in mN. The feature graph for this task and action is
9.1: Tracking a Guarded Move
179
0: (S, F, F) 1: (MF, F, M)
2: (S, Z, F) 3: (MC, Z, M)
4: (S, YZ, F) 5: (MC, YZ, M)
6: (S, 3, F)
7: (I, F, F) 8: (I, Z, F)
9: (I, YZ, F)
10: (I, 3, F)
Given the starting condition, the expected feature sequence is 0 ! 1 ! 8 ! 2 ! 3 ! 9 ! 4 ! 5 ! 10 ! 6. The impacts in the sequence could be missed which is accounted for in the feature graph. This sequence, with or without the impacts, was reliably found by the system. The errors that did occur happened when an unmodeled event occured, such as catching on the wood, which occasionally forced the system down the feature graph prematurely. The system can be made more robust by maintaining more paths.
The same experiment was also done with the addition of a feature for the (XZ) constraint presented by the second wall. In this case the decision process is being asked to determine if the second guarded move terminated on the XZ wall or the YZ wall. Under integral force control the decision processor would often transition to the XZ constraint model while still moving along the at Z constraint surface.
The problem occured because the force controller made the system move directly in the negative y direction. No motion or force information was gathered in the x direction. The decision processors was therefore forced to decide between Z constraint and XZ constraint without any signicant measurements. Any small burr or just the grain in the wood surface making up the Z constraint would trigger a transition and often the XZ constraint direction would be chosen.
This problem could be detected by a more detailed examination of the covariance matrix used in constraint estimation. When this problem arises, the covariance matrix will have only two signicant eigenvalues. The remaining four will be small in size. Two represent the true free directions, in the joint force and position space, and the four represent the lack of sucient measurements.
180
Chapter 9: Tasks In addition, this is not a problem intrinsic to the decision process. Rather, it is a higher level problem associated with action selection. The action selection processes must take into account not only the command required for reaching a given feature node but also all the features to which the system could next transition. If the features to which the system could transition can be disambiguated with the base action no exploration is necessary. However if the feature graph has multiplepossible new features, sucient exploration has to be added to the action. The need to explore can potentially be determined from the current markings on the feature graph and the transitions which can occur given the base action.However, more work is needed in control to make exploration actually work. The integral force controller was used for controlling the contact forces because it gives measurements that are easier to interpret than the position controller, because it does not under go stick-slip. Furthermore, it is much easier to command a force when the position of objects is not well known. However, exploration using this controller is dicult. Any exploratory position command will be rejected by the controller. If the position exploratory command attempts to move the robot in a direction in which the robot is trying to control to zero force no motion will occur. If the force exploratory command is added, the robot will undergo a random walk on the surface, due to friction, and it will be impossible to predict the expected feature transitions. It appears that additional work in force control is needed to develop a hybrid control technique that combines integral force control and impedance position control is needed.