Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot's operation that lead to variability in the resulting geometry. We propose a novel solution to these issues through the development of a Gaussian mixture kinematic model. We train a mixture density network to output a Gaussian mixture model representation of the robot geometry given the current tendon displacements. This model computes a probability distribution that is more representative of the true distribution of geometries at a given configuration than a model that outputs a single geometry, while also reducing the computation time. We demonstrate one use of this model through a trajectory optimization method that explicitly reasons about the workspace uncertainty to minimize the probability of collision.

翻译：腱驱动连续体机器人的运动学模型通常计算成本高昂、因未建模效应导致精度不足，或两者兼而有之。特别是，未建模效应会在机器人运行过程中产生不确定性，导致最终几何构型存在差异。针对这些问题，我们提出了一种新型解决方案——高斯混合运动学模型。通过训练混合密度网络，该模型可根据当前腱绳位移量输出机器人几何构型的高斯混合模型表示。相较于仅输出单一几何构型的传统模型，该模型不仅能够更准确地表征给定构型下几何分布的真实概率分布，还能显著降低计算时间。我们通过一种轨迹优化方法展示了该模型的应用：该方法显式考虑工作空间不确定性，以最小化碰撞概率。