This paper presents an approach to ensure conditions on Variable Impedance Controllers through the off-line tuning of the parameters involved in its description. In particular, we prove its application to term modulations defined by a Learning from Demonstration technique. This is performed through the assessment of conditions regarding safety and performance, which encompass heuristics and constraints in the form of Linear Matrix Inequalities. Latter ones allow to define a convex optimisation problem to analyse their fulfilment, and require a polytopic description of the VIC, in this case, obtained from its formulation as a discrete-time Linear Parameter Varying system. With respect to the current state-of-art, this approach only limits the term definition obtained by the Learning from Demonstration technique to be continuous and function of exogenous signals, i.e. external variables to the robot. Therefore, using a solution-search method, the most suitable set of parameters according to assessment criteria can be obtained. Using a 7-DoF Kinova Gen3 manipulator, validation and comparison against solutions with relaxed conditions are performed. The method is applied to generate Variable Impedance Controllers for a pulley belt looping task, inspired by the Assembly Challenge for Industrial Robotics in World Robot Summit 2018, to reduce the exerted force with respect to a standard (constant) Impedance Controller. Additionally, method agility is evaluated on the generation of controllers for one-off modifications of the nominal belt looping task setup without new demonstrations.

翻译：本文提出一种通过离线调参来确保变阻抗控制器描述参数满足条件的方法。具体而言，我们验证了该方法在基于示教学习技术定义的项调制中的应用。这通过对安全性和性能条件的评估实现，这些条件包含启发式规则和以线性矩阵不等式形式表达的约束。后者允许定义凸优化问题来分析其满足性，并需要变阻抗控制器的多胞描述——在本研究中通过将其建模为离散时间线性参数变化系统获得。相较于现有技术，本方法仅要求由示教学习技术获得的项定义为连续函数且依赖于外部信号（即机器人的外部变量）。因此，采用解搜索方法即可根据评估准则获得最合适的参数集。通过7自由度Kinova Gen3机械臂，我们进行了验证并与条件放宽的解决方案进行了对比。该方法被应用于生成用于滑轮皮带套环任务的变阻抗控制器——该任务受2018年世界机器人峰会工业机器人装配挑战赛启发，旨在相对于标准（恒定）阻抗控制器降低施加力。此外，还通过在没有新示教的情况下为标称皮带套环任务配置的单次修改生成控制器，评估了方法的敏捷性。