Abstract
A redundant manipulator usually has multiple kinematic solutions at the velocity level and can be used to optimize other criteria. Although the pseudo inverse of the Jacobian matrix generates a solution with the least 2 norm (LN), it does not consider other constraints imposed by the system or the environment. The general weighted least norm (GWLN) method handles these general constraints via the concept of virtual joints, but this is not always feasible when the number of constraints exceeds the degrees of freedom. This paper proposes a unified weighted least norm method (UWLN) to unify the LN and the GWLN methods. The UWLN method merges the constraint tasks into a quadratic criterion that poses no limitations on the number of constraint tasks. It also generates a least 2 norm solution when all constraints are deactivated, thereby unifying the LN and GWLN methods. A comparative simulation on a 7-DoF planar manipulator demonstrates the validity of the algorithm.
Highlights
Manipulators are today widely used in both industry manufacture and services in daily life, e.g., welding, spraypainting, polishing, surgery, etc
The unified weighted least norm method In the previous section, we discussed the defects of the general weighted least norm (GWLN) method, which mainly result from the construction
The criterion matrix in the unified weighted least norm (UWLN) method is capable of combining arbitrary con‐ straint tasks and always has full rank, which guarantees the numerical stability
Summary
Manipulators are today widely used in both industry manufacture and services in daily life, e.g., welding, spraypainting, polishing, surgery, etc. Zhang solved the quadratic programming problem through an evolving dynamic system based on neural networks and discovered the joint torque constraint and obstacle avoidance [9, 10, 11] These QP-based methods do not address the case when the constraint task conflicts with the manipulation task, which leads to an empty feasible set. To improve the performance of GWLN method, in this paper, we solved the constrained control problem via a unified weighted least norm (UWLN) method. The criterion matrix coincides with the criterion of the LN method when all the constraint tasks are not activated, which establishes a smooth transition between the LN solution and the constrained solution This approach proves that the unified weighted least norm method can accomplish the constraint tasks as well as the GWLN method.
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