Multi-backbone continuum robots demonstrated potentials for dexterous manipulation with proper payload capability in minimally invasive surgeries. Most prior works assume constant curvature shapes of the continuum segments in the modeling and control of the multi-backbone continuum robots. The actuation coupling effects between adjacent continuum segments and the segments’ variable curvature shapes under environmental interactions have not been fully addressed by a static-kinematic model specifically for multi-backbone continuum robots. This letter hence proposes a variable curvature model for multi-backbone continuum robots with relatively low bending curvature based on the Cosserat rod theory. The model focuses on the major factors that affect the robot's shape: the length-prescribed push-pull actuation, the elastic elongation of the backbone rods, and the external loads. With five assumptions made to simplify the constraints in the multi-backbone continuum robot, a compact statics-kinematics formulation is derived with computational performance acceptable for real-time control. Experiments were conducted on a continuum robotic system to quantify the modeling accuracy and computational efficiency. The proposed model was shown to have substantially improved accuracy over the constant curvature model. The average computational time for solving the inverse kinematics was 0.7ms on a 2.6 GHz Intel i7-5600U platform, which is promising for real-time control.

中文翻译：

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多骨干连续体机器人的可变曲率模型，用于说明段间耦合和外部干扰

多骨干连续体机器人在微创手术中展示了具有适当有效载荷能力的灵巧操作的潜力。大多数现有工作在多骨干连续体机器人的建模和控制中假设连续体段的曲率形状恒定。专门针对多骨干连续体机器人的静态运动模型尚未完全解决相邻连续体节段和各节段的可变曲率形状之间的致动耦合效应。因此，这封信提出了基于Cosserat杆理论的，具有相对较低弯曲曲率的多骨干连续体机器人的可变曲率模型。该模型着重于影响机器人形状的主要因素：长度规定的推拉驱动，骨架杆的弹性伸长以及外部载荷。通过简化五个假设来简化多主干连续体机器人中的约束条件，得出了紧凑的静态运动学公式，其计算性能可以接受实时控制。在连续机器人系统上进行了实验，以量化建模的准确性和计算效率。所提出的模型显示出比等曲率模型具有显着提高的精度。在2.6 GHz Intel i7-5600U平台上，求解逆运动学的平均计算时间为0.7毫秒，这有望实现实时控制。推导了紧凑的静力学运动学公式，其计算性能可以接受实时控制。在连续机器人系统上进行了实验，以量化建模的准确性和计算效率。所提出的模型显示出比等曲率模型具有显着提高的精度。在2.6 GHz Intel i7-5600U平台上，求解逆运动学的平均计算时间为0.7毫秒，这有望实现实时控制。推导了紧凑的静力学运动学公式，其计算性能可以接受实时控制。在连续机器人系统上进行了实验，以量化建模的准确性和计算效率。所提出的模型显示出比等曲率模型具有显着提高的精度。在2.6 GHz Intel i7-5600U平台上，求解逆运动学的平均计算时间为0.7毫秒，这有望实现实时控制。