A Mode-Switcher-Based Neural Solution to Linearly Constrained Systems Applied to Robot Obstacle Avoidance

Abstract

Time-variant linear equality and inequality (TVLEI) play crucial roles in various practical scenarios. Existing zeroing neural networks (ZNNs) have been designed to handle either time-variant linear equality or time-variant linear inequality separately. However, they suffer from shortcomings such as reducing the region of feasible solutions and introducing additional neurons when dealing with TVLEI. To overcome these challenges, this article introduces a new ZNN that incorporates projection operators capable of transforming inequality constraints into equality constraints. In general, projection operators are considered unsuitable for ZNN design because they are not differentiable everywhere. This article overcomes this issue by introducing the upper right-hand Dini derivative. By employing the Dini derivative of the projection operator as a mode switcher, the proposed mode switcher-based ZNN (MS-ZNN) is derived. Through the mode switchers, the MS-ZNN can dynamically switch control modes based on the satisfaction of the inequality constraints in TVLEI. Comparative validations highlight the effectiveness of the MS-ZNN, simultaneously showcasing its strengths such as reliable problem-solving ability, exceptional solution accuracy and proficient multitasking capability. To demonstrate practical applications, the MS-ZNN is applied to both the kinematic control and the dynamic control of a Franka Emika Panda robot, enabling tasks involving path tracking and obstacle avoidance.