通过Sobolev范数限制碰撞力
Bounded Collision Force by the Sobolev Norm
AI总结：
本文提出利用Sobolev范数作为系统范数，为动态系统中的最大碰撞力提供严格界限，通过实验和仿真验证了该方法在分析机器人碰撞力与控制策略、关节灵活性及末端执行器柔顺性之间的关系方面的有效性。
摘要：
机器人与环境或人类接触时可能产生安全风险，包括过大的碰撞力。尽管文献中有关于机器人惯性、相对速度和界面刚度对碰撞影响的实验研究，但关于最大碰撞力的分析模型仍局限于简化质量-弹簧机器人模型。该简化模型限制了对控制（力/扭矩、阻抗或顺应性）或柔顺机器人（关节和末端执行器柔顺性）的分析。本文将Sobolev范数适配为系统范数，为一般动态系统中刚度元件的最大力提供严格界限，允许使用更精确的模型和反馈控制进行碰撞研究。Sobolev范数可通过转换系统的$\mathcal{H}_2$范数找到，允许高效计算、连接现有控制理论并合成控制器以最小化碰撞力。Sobolev范数首先通过顺应性控制机器人进行实验验证，然后在模拟线性柔性关节机器人中进行验证。随后，它被用于研究控制、关节灵活性和末端执行器柔顺性对碰撞的影响，并展示了碰撞性能与环境估计不确定性之间的权衡。
英文摘要：
A robot making contact with an environment or human presents potential safety risks, including excessive collision force. While experiments on the effect of robot inertia, relative velocity, and interface stiffness on collision are in literature, analytical models for maximum collision force are limited to a simplified mass-spring robot model. This simplified model limits the analysis of control (force/torque, impedance, or admittance) or compliant robots (joint and end-effector compliance). Here, the Sobolev norm is adapted to be a system norm, giving rigorous bounds on the maximum force on a stiffness element in a general dynamic system, allowing the study of collision with more accurate models and feedback control. The Sobolev norm can be found through the $\mathcal{H}_2$ norm of a transformed system, allowing efficient computation, connection with existing control theory, and controller synthesis to minimize collision force. The Sobolev norm is validated, first experimentally with an admittance-controlled robot, then in simulation with a linear flexible-joint robot. It is then used to investigate the impact of control, joint flexibility and end-effector compliance on collision, and a trade-off between collision performance and environmental estimation uncertainty is shown.
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