Manipulator Redundancy Analysis

933 Words2 Pages

2.3 REDUNDANCY RESOLUTION
Manipulator redundancy resolution is a way to specify a functional form of the redundant degrees of freedom based on some objective functions such that, among the infinite number of choices, a specific solution of the inverse kinematics problem is determined. This has been a research topic that has attracted considerable attention in recent years [20][30], and has resulted in a number of different approaches for redundancy resolution.
In order to be able to analyze and evaluate the methods for resolving kinematic redundancy in a systematic way, it is necessary to classify them according to some common criteria, properties or underlying mathematical formulations. There are a number of ways for classifying the methodologies which resolve kinematic redundancy. For example, one can classify the methods based on performance criteria such as kinematic optimality criteria (e.g. manipulability index [40]) or kinetic criteria (e.g. joint torques). Alternatively, one may borrow terminologies from optimization theory and consider a classification into two classes that utilize (l) Local optimization approaches and (2) Global optimization approaches. These classifications may have some advantages, but they have no direct connection with the control strategies used for redundant manipulators. Since the aim of this thesis is to develop control strategies for redundant manipulators. We shall consider another classification where the terminology is based on control techniques. In particular, the classification is based on control strategies that incorporate end-effector measurements such as those based on resolved-position, resolved-velocity, and resolved-acceleration. Depending on which equation (i.e., equation (2.2.1), ...

... middle of paper ...

...and a homogeneous equation Zh = 0, where h is the gradient vector of the constraint function. The matrix Z is composed of the n –m linearly independent vectors which span the null space of the manipulator's Jacobian matrix. Therefore, the homogeneous equation characterizes the self-motion of the redundant manipulator. The n algebraic equations can be solved iteratively using numerical methods. It should be noted that the formulation of redundancy resolution in this approach is very versatile since the matrix Z depends only on the manipulator Jacobian while the vector h depends only on the desired performance criteria. A potential drawback of the method is the computational complexity since the definition of Z involves selecting and inverting a full rank submatrix based on the manipulator Jacobian Je. Some other approaches in this category can be found in [1] [16].

Open Document