# Handling robot constraints within a Set-Based Multi-Task Priority Inverse Kinematics Framework

## TL;DR

This paper presents a framework that integrates set-based multi-task priority inverse kinematics with constraint handling, enabling real-time management of safety and operational constraints in redundant robotic systems.

## Contribution

It introduces a novel task prioritization and design approach within the set-based multi-task framework to handle multiple constraints simultaneously in real-time robotic control.

## Key findings

- Effective handling of joint limits and singularities at high priority.
- Successful real-time implementation on a 7DOF robot demonstrating constraint management.
- Enhanced safety and operational performance in inverse kinematics tasks.

## Abstract

Set-Based Multi-Task Priority is a recent framework to handle inverse kinematics for redundant structures. Both equality tasks, i.e., control objectives to be driven to a desired value, and set-bases tasks, i.e., control objectives to be satisfied with a set/range of values can be addressed in a rigorous manner within a priority framework. In addition, optimization tasks, driven by the gradient of a proper function, may be considered as well, usually as lower priority tasks. In this paper the proper design of the tasks, their priority and the use of a Set-Based Multi-Task Priority framework is proposed in order to handle several constraints simultaneously in real-time. It is shown that safety related tasks such as, e.g., joint limits or kinematic singularity, may be properly handled by consider them both at an higher priority as set-based task and at a lower within a proper optimization functional. Experimental results on a 7DOF Jaco$^2$