A White-Noise-On-Jerk Motion Prior for Continuous-Time Trajectory Estimation on SE(3)

Simultaneous trajectory estimation and mapping (STEAM) offers an efficient approach to continuous-time trajectory estimation, by representing the trajectory as a Gaussian process (GP). Previous formulations of the STEAM framework use a GP prior that assumes white-noise-on-acceleration, with the prior mean encouraging constant body-centric velocity. We show that such a prior cannot sufficiently represent trajectory sections with non-zero acceleration, resulting in a bias to the posterior estimates. This paper derives a novel motion prior that assumes white-noise-on-jerk, where the prior mean encourages constant body-centric acceleration. With the new prior, we formulate a variation of STEAM that estimates the pose, body-centric velocity, and body-centric acceleration. By evaluating across several datasets, we show that the new prior greatly outperforms the white-noise-on-acceleration prior in terms of solution accuracy.Comment: To appear in IEEE Robotics and Automation Letters (RA-L). 8 pages, 5 figure

Random Fourier Features based SLAM

This work is dedicated to simultaneous continuous-time trajectory estimation and mapping based on Gaussian Processes (GP). State-of-the-art GP-based models for Simultaneous Localization and Mapping (SLAM) are computationally efficient but can only be used with a restricted class of kernel functions. This paper provides the algorithm based on GP with Random Fourier Features(RFF)approximation for SLAM without any constraints. The advantages of RFF for continuous-time SLAM are that we can consider a broader class of kernels and, at the same time, significantly reduce computational complexity by operating in the Fourier space of features. The additional speedup can be obtained by limiting the number of features. Our experimental results on synthetic and real-world benchmarks demonstrate the cases in which our approach provides better results compared to the current state-of-the-art

Active Area Coverage from Equilibrium

This paper develops a method for robots to integrate stability into actively seeking out informative measurements through coverage. We derive a controller using hybrid systems theory that allows us to consider safe equilibrium policies during active data collection. We show that our method is able to maintain Lyapunov attractiveness while still actively seeking out data. Using incremental sparse Gaussian processes, we define distributions which allow a robot to actively seek out informative measurements. We illustrate our methods for shape estimation using a cart double pendulum, dynamic model learning of a hovering quadrotor, and generating galloping gaits starting from stationary equilibrium by learning a dynamics model for the half-cheetah system from the Roboschool environment.Comment: 16 page

Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.Comment: The International Journal of Robotics Research (IJRR), 2018, Volume 37, Issue 1

Adaptive Trajectory Estimation with Power Limited Steering Model under Perturbation Compensation

Trajectory estimation of maneuvering objects is applied in numerous tasks like navigation, path planning and visual tracking. Many previous works get impressive results in the strictly controlled condition with accurate prior statistics and dedicated dynamic model for certain object. But in challenging conditions without dedicated dynamic model and precise prior statistics, the performance of these methods significantly declines. To solve the problem, a dynamic model called the power-limited steering model (PLS) is proposed to describe the motion of non-cooperative object. It is a natural combination of instantaneous power and instantaneous angular velocity, which relies on the nonlinearity instead of the state switching probability to achieve switching of states. And the renormalization group is introduced to compensate the nonlinear effect of perturbation in PLS model. For robust and efficient trajectory estimation, an adaptive trajectory estimation (AdaTE) algorithm is proposed. By updating the statistics and truncation time online, it corrects the estimation error caused by biased prior statistics and observation drift, while reducing the computational complexity lower than O(n). The experiment of trajectory estimation demonstrates the convergence of AdaTE, and the better robust to the biased prior statistics and the observation drift compared with EKF, UKF and sparse MAP. Other experiments demonstrate through slight modification, AdaTE can also be applied to local navigation in random obstacle environment, and trajectory optimization in visual tracking.Comment: 19 pages, 7 figure

Active Learning of Dynamics for Data-Driven Control Using Koopman Operators

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free-fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems.Comment: 14 pages, In Pres