Control and Planning of Variable Stiffness Links for Inherently Safe Physical Human Robots Interaction #

Traditional industrial robots may not suitable for direct interaction with human workers in the same workspace. Recently, researchers have shown increasing interest in studying collaborative robot (corobot) which is designed for working with human side by side. Therefore, the safety becomes a critical issue considering the possibility of physical human robot interaction (pHRI). The safety of pHRI can be achieved in different ways. Typically, an impact between a robot and a human can be divided into three phases: pre-impact phase, impact phase, and post-impact phase. For impact phase and post-impact phase, strategies like collision detection and reaction [1] [2] [3] can significantly reduce injury severity. However, it is worth to mention that such active strategies for impact phase and post-impact phase cannot decrease the injury severity of the impact in some situations such as high speed and rigid impact [4]. To achieve inherent safety, only measures in the impact phase and post-impact phase are not enough. New mechanical designs and control approaches for the pre-impact phase is also needed to enhance safety. To address the preimpact design problem, methods such as obstacle avoidance [5] [6], mechanical design optimization [7] [8] and variable stiffness concept [2] [9] [10] [11] are proposed. Among those approaches, variable stiffness link (VSL) is a synthesis of software (control, planning) and hardware (mechanical design) which is the focus in this study. By tuning the link stiffness, VSL can compromise safety and efficiency in a better way. A low-stiffness configuration allows a faster motion while the safety is ensured. A high-stiffness configuration attenuates the vibration thus improve the positioning performance. However, the control design for safe VSL robots is quite a challenge due to its complicated dynamics and safety requirements. For safe robots with VSL, control objectives and their challenges can be summarized as follows. (1) Tracking of the desired joint trajectory (uncertainties and disturbances). (2) Vibration suppression (varying flexibility). (3) Inherent safety (pre-impact, impact, and post-impact phase). To address these challenges, in this note, (1) we develop a dynamics model of VSL robots by the pseudo-rigid-body model (PRBM) [12] [13]; (2) we formulate the feedback linearization to VSL robots, inspired by previous works on conventional flexible robots such as [14] [15]. To improve the robustness in engineering practice, the linearization-based controller is further enhanced by using an extended state observer (ESO). A deflection feedback is designed based on the singular perturbation theory to achieve better vibration suppression; (3) For the inherent safety of the VSL robots, we propose a trajectory planning method based on optimal control theory. By converting the safety criterion such as human injury criterion (HIC) to velocity limit, the trajectory planning problem is transferred to a constrained time-optimal control problem with input constraints and state constraints [9]. In this note, we give a closed-form solution to the rest-to-rest motion trajectory based on optimal control theory.