论文标题
连续机器人多项式曲率状态空间中的随机自适应估计
Stochastic Adaptive Estimation in Polynomial Curvature Shape State Space for Continuum Robots
论文作者
论文摘要
在连续机器人技术中，实时鲁棒形状估计对于涉及复杂环境中物理操作的计划和控制任务至关重要。在本文中，我们提出了专门为连续机器人设计的新型随机观察者形状估计框架。形状状态空间由多项式的模态系数独特地表示，该系数通过利用多项式曲率运动学（PCK）来描述沿Arclength的曲率分布。我们的框架过程从有限的离散位置，方向或构成传感器中嘈杂测量，以稳健地估算形状状态。我们得出了一种新型的噪声加权可观察性矩阵，对不同传感器配置下的可观察性变化进行了详细的评估。为了克服单个模型的局限性，我们的观察者采用了相互作用的多重模型（IMM）方法，并加上扩展的卡尔曼过滤器（EKFS），以混合不同顺序的多项式曲率模型。植根于马尔可夫过程的IMM方法通过基于实时模型概率动态适应不同的多项式订单来有效地管理多个模型方案。这种适应性是确保在各种条件下机器人行为的稳健形状估计的关键。在模拟研究和实验验证的支持下，我们的全面分析证实了我们方法的鲁棒性和准确性。
In continuum robotics, real-time robust shape estimation is crucial for planning and control tasks that involve physical manipulation in complex environments. In this paper, we present a novel stochastic observer-based shape estimation framework designed specifically for continuum robots. The shape state space is uniquely represented by the modal coefficients of a polynomial, enabled by leveraging polynomial curvature kinematics (PCK) to describe the curvature distribution along the arclength. Our framework processes noisy measurements from limited discrete position, orientation, or pose sensors to estimate the shape state robustly. We derive a novel noise-weighted observability matrix, providing a detailed assessment of observability variations under diverse sensor configurations. To overcome the limitations of a single model, our observer employs the Interacting Multiple Model (IMM) method, coupled with Extended Kalman Filters (EKFs), to mix polynomial curvature models of different orders. The IMM approach, rooted in Markov processes, effectively manages multiple model scenarios by dynamically adapting to different polynomial orders based on real-time model probabilities. This adaptability is key to ensuring robust shape estimation of the robot's behaviors under various conditions. Our comprehensive analysis, supported by both simulation studies and experimental validations, confirms the robustness and accuracy of our methods.
