Continuum manipulators offer intrinsic dexterity and safe geometric compliance for navigation within confined and obstacle-rich environments. However, their infinite-dimensional backbone deformation, unmodeled internal friction, and configuration-dependent stiffness fundamentally limit the reliability of model-based kinematic formulations, resulting in inaccurate Jacobian predictions, artificial singularities, and unstable actuation behavior. Motivated by these limitations, this work presents a complete model-less control framework that bypasses kinematic modeling by using an empirically initialized Jacobian refined online through differential convex updates. Tip motion is generated via a real-time quadratic program that computes actuator increments while enforcing tendon slack avoidance and geometric limits. A backbone tension optimization term is introduced in this paper to regulate axial loading and suppress co-activation compression. The framework is validated across circular, pentagonal, and square trajectories, demonstrating smooth convergence, stable tension evolution, and sub-millimeter steady-state accuracy without any model calibration or parameter identification. These results establish the proposed controller as a scalable alternative to model-dependent continuum manipulation in a constrained environment.

翻译：连续体机械臂凭借其固有的灵巧性和安全几何顺应性，在受限且障碍物密集的环境中展现出卓越的导航能力。然而，其无限维骨架变形、未建模的内部摩擦以及构型依赖的刚度从根本上限制了基于模型的运动学公式的可靠性，导致雅可比矩阵预测不准确、产生人为奇点以及驱动行为不稳定。针对这些局限性，本研究提出了一种完整的无模型控制框架，通过使用经验初始化的雅可比矩阵并在线进行差分凸优化更新，绕过了运动学建模过程。末端运动通过实时二次规划生成，该规划在计算执行器增量时同时满足肌腱松弛避免和几何约束。本文引入了骨架张力优化项，用于调节轴向载荷并抑制协同驱动压缩。该框架在圆形、五边形和正方形轨迹上进行了验证，展现出平滑收敛、稳定的张力演化以及亚毫米级的稳态精度，且无需任何模型校准或参数辨识。这些结果表明，所提出的控制器在受限环境中可作为依赖模型的连续体操作方法的可扩展替代方案。