Incorporating Control Inputs in Continuous-Time Gaussian Process State Estimation for Robotics

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. For example, in a mobile robot localization experiment with sparse landmark distance measurements and frequent odometry control inputs, our approach provides accurate trajectory estimates with root-mean-square errors around 3-4 cm and 4-5 degrees, even with time intervals up to five seconds between discrete estimation nodes, which significantly reduces computation time.