Continuous-time batch state estimation using Gaussian processes is an efficient approach to estimate the trajectories of robots over time. In the past, relatively simple physics-motivated priors have been considered for such approaches, using assumptions such as constant velocity or acceleration. This paper presents an approach to incorporating exogenous control inputs, such as velocity or acceleration commands, into the continuous Gaussian process state-estimation framework. It is shown that this approach generalizes across different domains in robotics, making it applicable to both the estimation of continuous-time trajectories for mobile robots and the estimation of quasi-static continuum robot shapes. Results show that incorporating control inputs leads to more informed priors, potentially requiring less measurements and estimation nodes to obtain accurate estimates. This makes the approach particularly useful in situations in which limited sensing is available.

翻译：采用高斯过程进行连续时间批量状态估计是一种高效估计机器人随时间轨迹的方法。以往此类方法通常考虑相对简单的物理驱动先验，例如采用恒定速度或恒定加速度等假设。本文提出了一种将外生控制输入（如速度或加速度指令）融入连续高斯过程状态估计框架的方法。研究表明，该方法可推广至机器人学的不同领域，既适用于移动机器人的连续时间轨迹估计，也适用于准静态连续体机器人形变估计。结果表明，融合控制输入能够构建信息更丰富的先验模型，从而可能以更少的测量数据和估计节点获得精确估计。这使得该方法在传感能力受限的场景中具有特殊应用价值。