Solving the singularity problem of non-redundant manipulators by constraint optimization

A solution to the singularity problem of a non-redundant robot is proposed by reformulating the inverse kinematic problem as a constraint optimization problem. The main idea is to allow a cartesian error in a given subspace in the vicinity of a singularity and to minimize this error subject to operational constraints such as maximum motor speeds. As a result, in every sampling instant a series of linear least squares problems with linear equality and inequality constraints have to be solved. This task can be carried out on a Pentium processor within a few milliseconds. The new method is demonstrated by real experiments with an industrial robot.

Authors

• Günter Schreiber
• Martin Otter
• Gerhard Hirzinger

Keywords

• Constraint optimization
• Jacobian matrices
• Robot kinematics
• Manipulator dynamics
• Subspace constraints
• Least squares methods
• Acceleration
• Aerodynamics
• Sampling methods
• Service robots
• Constrained Optimization
• Singularity Problem
• Optimization Problem
• Least Squares Regression
• Inequality Constraints
• Inverse Problem
• Equality Constraints
• Linear Constraints
• Linear Inequalities
• Least Squares Problem
• Operational Constraints
• Constraint Optimization Problem
• Linear Inequality Constraints
• Linear Least Squares Problem
• Numerical Solution
• Physical Limitations
• Jacobian Matrix
• Speed Limit
• Rank Deficiency
• Redundancy Problem
• Torque Limits
• Cartesian Position
• End-effector
• Switching Condition
• Iterative Point
• Joint Acceleration