Progress_Report-August 2nd-2011

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Meeting August 2nd 2011:

Meeting August 2 nd 2011 Aidin Foroughi

Repeating: Feature Switching Problem:

Repeating: Feature Switching Problem Simple switching rules for stability of the switching of reference features were given based on a multiple Lyaponuv function approach. Some issues with this approach is that: It’s based on the assumption that for each sub-system we are in the stable region around the equilibrium point. It can’t be used for the first time when we switch from the reference set Si to Sj ; It will only tell us if this switching is allowed next time we want to switch to Sj again. The rule is a sufficient condition not a necessary one. The rule can only help us rule out a certain number of transitions from what is possible; it doesn’t tell us which transition is the best. In the case where a transition is imposed by the circumstances of the problem, even if it’s not allowed based on this rule it doesn’t give us a solution in this condition.

Repeating: If the rule works:

Repeating: If the rule works Even if we stick to this rule, it’s based on the assumption that an unlimited field of view is available, which is not true. Therefore: Although the system is stable, transient effects may violate FOV constraint or other kinematic or dynamic constraints. A weighting approach is used generally in the literature to make the transitions smoother. In the following I will try to show how a weighting approach is related to a switching approach.

Barrier Lyapunov Function:

Barrier Lyapunov Function I read in this direction and while the approach is interesting there are two issues that doesn’t let us use this approach: This approach has been used in conjugation with a backstepping control scheme that uses the lyapunov function in the loop. Otherwise, the information from the barriers can’t be used for control. There is a feasibility check stage, which tries to solve the system to see if the constraints have a feasible solution. This solution is not possible for the IBVS problem since the nonlinear system equations are not available beforehand. (we find the interaction matrix as we go along) Another problem issue is that the barrier approach may not extend well in the case of switching because when we switch the new lyapunov function maybe outside of the barriers.

Simulation Framework:

Simulation Framework On Monday, I compiled the ViSP library and then compiled and ran a few demos. ViSP is a powerful framework which already has many components we need:

Simulation Framework:

Simulation Framework However, for the prototyping and quick proofs of concept it’s too complicated and it takes quite sometime to start a simulation. But it is definitely a candidate for the final implementation of the project. I then used a Toolbox for visual servoing . It has some nice classes and a couple of useful simulink blocks. The following simulations have been done in MATLAB using this toolbox.

Practical results on switching:

Practical results on switching I performed several IBVS tasks using the constant interaction matrix (of the reference image) and an online accurate interaction matrix. This was done with 5 features. Next, I chose 3 features among the 5 and then switched this selection in each step. This has to give the worst stability situation since the faster we switch the less time for the more the possibility of instability (in fact, for the case of switched linear system a lower switching time limit can be derived that if we switch slower than that we’ll be stable: dwell time) Then I did the same for a selection of 4 out of 5. Here is the results on the velocity command sent to the controller.

Control loop:

Control loop The original Control loop, IBVS and J determined using the reference image.

Control loop:

Control loop Modified control loop with feature seletion

IBVS, J according to S*:

IBVS, J according to S* Switching the selection of 3 out of 5.

IBVS, J according to S*:

IBVS, J according to S* Switching the selection of 4 out of 5.

Effect on image trajectories and error:

Effect on image trajectories and error But the errors and feature trajectories are smooth!

IBVS, J determined online:

IBVS, J determined online Switching the selection of 3 out of 5.

Effect on image trajectories and error:

Effect on image trajectories and error Again, the physical output is smooth

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