In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)$times$R3and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to make a better choice for the ME task. In addition, unique to our framework, we derive the kinematic models with theclosed-form temporal derivatives of the local variables ofSO(3) and SE(3), which so far has only been approximated based on Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available athttps://github.com/brytsknguyen/gptr.

Robot navigation in dense human crowds poses a significant challenge due to the complexity of human behavior in dynamic and obstacle-rich environments. In this work, we propose a dynamic weight adjustment scheme using a neural network to predict the optimal weights of objectives in an optimization-based motion planner. We adopt a spatial-temporal trajectory planner and incorporate diverse objectives to achieve a balance among safety, efficiency, and goal achievement in complex and dynamic environments. We design the network structure, observation encoding, and reward function to effectively train the policy network using reinforcement learning, allowing the robot to adapt its behavior in real time based on environmental and pedestrian information. Simulation results show improved safety compared to the fixed-weight planner and the state-of-the-art learning-based methods, and verify the ability of the learned policy to adaptively adjust the weights based on the observed situations. The feasibility of the approach is demonstrated in a navigation task using an autonomous delivery robot across a crowded corridor over a 300 m distance. Video: https://youtu.be/nSCbNaaF_VM