Kinematics of flexible backbone continuum robots is highly non linear and its complexity quickly escalates with the number of sections of the robot, which is usually more than three. This paper introduces a kinematic modelling of actuation and configuration spaces that greatly simplifies the computational requirements compared to the commonly used Piecewise Constant Curvature Kinematics which results in a faster algorithm at a rate proportional to the number of sections. This new algorithm is firstly developed for Twin Pivot Compliant Joint continuum robots but then extended to a general single neutral axis backbone configuration, both achieving a very low error of approximation (0.7% for the prototype developed), which results in several advantages such as the avoidance of highly non-linear functions and singularities, great reduction of computational complexity and an user-friendly graphical representation to help operation and status monitoring of this kind of robots. Moreover, a slender, small diameter and hyper-redundant (175 mm length, 6 mm diameter, 10 Degrees of Freedom) continuum robot prototype is developed and tested in a real-case industrial application for inspection and repair of aero engines in order to validate the proposed model.

柔性骨干连续体机器人的运动学是高度非线性的，并且其复杂度会随着机器人部分的数量迅速增加，通常为三个以上。本文介绍了驱动空间和配置空间的运动学模型，与常用的分段恒定曲率运动学相比，它大大简化了计算要求，从而以与截面数成比例的速率产生了更快的算法。这种新算法首先为Twin Pivot Compliant联合连续体机器人开发，然后扩展到通用的单个中性轴骨架结构，都实现了非常低的近似误差（对于所开发的原型为0.7％），这带来了以下优点：避免高度非线性的函数和奇点，大大降低了计算复杂性，并提供了易于使用的图形表示形式，以帮助此类机器人进行操作和状态监控。此外，还开发了细长，小直径和超冗余（175毫米长，6毫米直径，10个自由度）的连续体机器人原型，并在实际工业应用中对其进行了测试，以检验和维修航空发动机，以验证建议的模型。