In the field of Learning from Demonstration (LfD), Dynamical Systems (DSs) have gained significant attention due to their ability to generate real-time motions and reach predefined targets. However, the conventional convergence-centric behavior exhibited by DSs may fall short in safety-critical tasks, specifically, those requiring precise replication of demonstrated trajectories or strict adherence to constrained regions even in the presence of perturbations or human intervention. Moreover, existing DS research often assumes demonstrations solely in Euclidean space, overlooking the crucial aspect of orientation in various applications. To alleviate these shortcomings, we present an innovative approach geared toward ensuring the safe execution of learned orientation skills within constrained regions surrounding a reference trajectory. This involves learning a stable DS on SO(3), extracting time-varying conic constraints from the variability observed in expert demonstrations, and bounding the evolution of the DS with Conic Control Barrier Function (CCBF) to fulfill the constraints. We validated our approach through extensive evaluation in simulation and showcased its effectiveness for a cutting skill in the context of assisted teleoperation.

翻译：在示范学习（LfD）领域，动力系统（DS）因其能够生成实时运动并到达预设目标而受到广泛关注。然而，传统DS所展现的以收敛为中心的行为在安全关键型任务中可能有所不足，尤其是在需要精确复现示范轨迹或严格遵循受限区域（即使存在扰动或人为干预）的任务中。此外，现有DS研究通常假设示范仅在欧氏空间中进行，忽略了诸多应用中定向这一关键方面。为解决这些不足，我们提出了一种创新方法，旨在确保在参考轨迹周围的受限区域内安全执行学习到的定向技能。该方法包括：在SO(3)上学习稳定的动力系统，从专家演示中观测到的变异性中提取时变锥形约束，并利用锥形控制屏障函数（CCBF）约束DS的演化以满足约束条件。我们通过仿真中的广泛评估验证了该方法，并在辅助遥操作背景下展示了其在切割技能中的有效性。