Convex Geometric Motion Planning on Lie Groups via Moment Relaxation

This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as semidefinite programming (SDP). Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not properly deal with the configuration space of the 3D rigid body; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space in our formulation and apply the variational integrator to formulate the forced rigid body systems as quadratic polynomials. Then we leverage Lasserre's hierarchy to obtain the globally optimal solution via SDP. By constructing the motion planning problem in a sparse manner, the results show that the proposed algorithm has \emph{linear} complexity with respect to the planning horizon. This paper demonstrates the proposed method can provide rank-one optimal solutions at relaxation order two for most of the testing cases of 1) 3D drone landing using the full dynamics model and 2) inverse kinematics for serial manipulators.Comment: Accepted to Robotics: Science and Systems (RSS), 202

Fully Proprioceptive Slip-Velocity-Aware State Estimation for Mobile Robots via Invariant Kalman Filtering and Disturbance Observer

This paper develops a novel slip estimator using the invariant observer design theory and Disturbance Observer (DOB). The proposed state estimator for mobile robots is fully proprioceptive and combines data from an inertial measurement unit and body velocity within a Right Invariant Extended Kalman Filter (RI-EKF). By embedding the slip velocity into $\mathrm{SE}_3(3)$ Lie group, the developed DOB-based RI-EKF provides real-time accurate velocity and slip velocity estimates on different terrains. Experimental results using a Husky wheeled robot confirm the mathematical derivations and show better performance than a standard RI-EKF baseline. Open source software is available for download and reproducing the presented results.Comment: github repository at https://github.com/UMich-CURLY/slip_detection_DOB. arXiv admin note: text overlap with arXiv:1805.10410 by other author

An Error-State Model Predictive Control on Connected Matrix Lie Groups for Legged Robot Control

This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra. Moreover, given an initial condition, the linearized tracking error dynamics and equations of motion are globally valid and evolve independently of the system trajectory. By exploiting the symmetry of the problem, the proposed approach shows faster convergence of rotation and position simultaneously than the state-of-the-art geometric variational MPC based on variational-based linearization. Numerical simulation on tracking control of a fully-actuated 3D rigid body dynamics confirms the benefits of the proposed approach compared to the baselines. Furthermore, the proposed MPC is also verified in pose control and locomotion experiments on a quadrupedal robot MIT Mini Cheetah.Comment: Proceedings of the 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2022

Co-estimation of lithium-ion battery state of charge and state of temperature based on a hybrid electrochemical-thermal-neural-network model

Battery modeling and state estimation are critical to the battery safety and vehicle driving range. Currently, electrochemical mechanism based models require huge computation effort for solving partial differential equations, equivalent circuit models do not consider actual battery mechanism, while machine learning models are lack of generalization ability due to their data-driven nature. All these problems bring the challenges to guarantee the model effectiveness in wide temperature and large current conditions. To estimate the battery state of charge (SOC) and state of temperature (SOT) under these conditions, an electrochemical-thermal-neural-network (ETNN) model is formulated in this paper. Specifically, a simplified single particle model and a lumped thermal model are served as the sub-models of ETNN to predict core temperature and provide approximate terminal voltage. Then a neural network is incorporated to enhance the performance of sub-models. According to the extensive experiments, ETNN model is able to accurately estimate battery voltage and core temperature under the ambient temperatures of -10–40 °C and the discharge rate of 10-C. After that, an unscented Kalman filter (UKF) is integrated with ETNN to achieve reliable co-estimation of SOC-SOT. Experimental results illustrate that proposed ETNN-UKF can rapidly eliminate initial errors and provide satisfactory co-estimation performance