Resolving kinematic redundancy of a robot using a quadratically constrained optimization technique

The constraints on the physical limit should be considered in a kinematic redundancy resolution problem of a robot. This paper proposes a new optimization scheme to resolve kinematic redundancy of the robot while considering physical constraints. In the proposed scheme, quadratic inequality constraints are used in place of linear inequality constraints, thus a quadratically constrained optimization technique is applied to resolve the redundancy. It is shown that the use of quadratic inequality constraints considerably reduces the number of constraints. Therefore, the proposed method reduces the problem size considerably and makes the problem simple resulting in computational efficiency. A numerical example of a 4-link planar redundant robot is included to demonstrate the efficiency of the proposed optimization technique. In this example, simulation results using the proposed method and another well-known method are compared and discussed.

Mode Shape Expansion Techniques for Model Error Localization and Damage Detection

Several methods for mode shape expansion are investigated. The most popular methods use the dynamic equations of motions to obtain direct solutions, or use orthogonal projections. Both approaches can also be formulated as constrained optimization problems. To account for uncertainties in the measurements and in the prediction, a new expansion technique based on least squares minimization with quadratic inequality constraints (LSQI) is proposed. Each modal expansion technique is evaluated with experimental data obtained on the Micro-Precision Interferometer testbed, using both the pre-test and updated analytical models. The robustness of these methods is verified with respect to measurement noise and model error. It is shown that the proposed LSQI method has the best performance and can reliably predict mode shapes, and can be used to locate damage elements, even in very adverse situations. A new LSQI algorithm is also proposed which significantly decreases the solution time.