Kinematic Control With Singularity Avoidance for Redundant Robots: A Regularized Condition Number-Based Optimization Method

Avoiding singular configurations is directly related to the successful completion of a task by a robot. Existing indices struggle to accurately characterize the singular level of configurations. This article proposes a new kinematic index, called the regularized condition number, for singularity avoidance by combining the condition number with a minimum singular value penalty. Accordingly, for singularity avoidance in redundant robots, a regularized condition number optimization-based (RCNO) scheme is constructed from a dynamic evolution perspective. Furthermore, to improve the control accuracy of redundant robots near singular configurations, an adaptive double-projection neural dynamics (ADND) model is designed to solve the RCNO scheme, transforming the optimization problem into the search for an equilibrium point in a dynamical system. The proposed ADND model enforces multilevel joint constraints by utilizing the double-projection function, and an adaptive mechanism is designed in the model to cope with the numerical instability near singular configurations. Theoretical analyses verify the constraint-handling capability and convergence of the ADND model. Simulations, comparisons, and experiments confirm the effectiveness, superiority, and practicality of the proposed RCNO scheme and ADND model.