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This article presents an invariant extended Kalman filter (InEKF) approach for estimating the relative pose and linear velocity of ground robots—either legged or wheeled—using an inertial measurement unit (IMU) attached to the robot, encoders, and an external IMU placed on the moving ground. The approach explicitly accounts for ground motion in noninertial environments, such as ships or airplanes, where the ground rotates or accelerates in the inertial frame. Unlike previous methods, it does not rely on known ground pose. This consideration introduces complexity due to the nonlinear dynamics and kinematics of the reference frame. Despite this complexity, the proposed filter, based on the InEKF methodology, includes a process model that partially satisfies the group affine condition. The leg odometry-based measurement model meets the right-invariant observation form for deterministic scenarios, though the wheel odometry model does not. Observability analysis demonstrates that all state variables are observable during a broad range of ground motions, overcoming the partial observability limitations of previous filters. Experiments on a Digit humanoid robot and a Jackal wheeled robot verify the filter’s effectiveness across various ground motions. 

This paper reports a novel result: with proper robot models based on geometric mechanics, one can formulate the kinodynamic motion planning problems for rigid body systems as exact polynomial optimization problems. Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not parameterize 3D rigid body motion efficiently; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space and apply the variational integrator to formulate the forced rigid body dynamics as quadratic polynomials. Then, we leverage Lasserre’s hierarchy of moment relaxation to obtain the globally optimal solution via semidefinite programming. By leveraging the sparsity of the motion planning problem, the proposed algorithm has linear complexity with respect to the planning horizon. This paper demonstrates that the proposed method can provide globally optimal solutions or certificates of infeasibility at the second-order relaxation for 3D drone landing using full dynamics and inverse kinematics for serial manipulators. Moreover, we extend the algorithms to multi-body systems via the constrained variational integrators. The testing cases on cart-pole and drone with cable-suspended load suggest that the proposed algorithms can provide rank-one optimal solutions or nontrivial initial guesses. Finally, we propose strategies to speed up the computation, including an alternative formulation using quaternion, which provides empirically tight relaxations for the drone landing problem at the first-order relaxation. 

Partial point cloud registration is a challenging problem in robotics, especially when the robot undergoes a large transformation, causing a significant initial pose error and a low overlap between measurements. This letter proposes exploiting equivariant learning from 3D point clouds to improve registration robustness. We propose SE3ET, an SE(3)-equivariant registration framework that employs equivariant point convolution and equivariant transformer designs to learn expressive and robust geometric features. We tested the proposed registration method on indoor and outdoor benchmarks where the point clouds are under arbitrary transformations and lowoverlapping ratios.We also provide generalization tests and run-time performance. 

This work investigates the robot state estimation problem within a non-inertial environment. The proposed state estimation approach relaxes the common assumption of static ground in the system modeling. The process and measurement models explicitly treat the movement of the non-inertial environments without requiring knowledge of its motion in the inertial frame or relying on GPS or sensing environmental landmarks. Further, the proposed state estimator is formulated as an invariant extended Kalman filter (InEKF) [1] with the deterministic part of its process model obeying the groupaffine property, leading to log-linear error dynamics. The observability analysis confirms the robot’s pose (i.e., position and orientation) and velocity relative to the non-inertial environment are observable under the proposed InEKF. 

This paper reports on developing a real-time invariant proprioceptive robot state estimation framework called DRIFT. A didactic introduction to invariant Kalman filtering is provided to make this cutting-edge symmetry-preserving approach accessible to a broader range of robotics applications. Furthermore, this work dives into the development of a proprioceptive state estimation framework for dead reckoning that only consumes data from an onboard inertial measurement unit and kinematics of the robot, with two optional modules, a contact estimator and a gyro filter for low-cost robots, enabling a significant capability on a variety of robotics platforms to track the robot's state over long trajectories in the absence of perceptual data. Extensive real-world experiments using a legged robot, an indoor wheeled robot, a field robot, and a full-size vehicle, as well as simulation results with a marine robot, are provided to understand the limits of DRIFT. 

n this article, we present a novel and flexible multitask multilayer Bayesian mapping framework with readily extendable attribute layers. The proposed framework goes beyond modern metric-semantic maps to provide even richer environmental information for robots in a single mapping formalism while exploiting intralayer and interlayer correlations. It removes the need for a robot to access and process information from many separate maps when performing a complex task, advancing the way robots interact with their environments. To this end, we design a multitask deep neural network with attention mechanisms as our front-end to provide heterogeneous observations for multiple map layers simultaneously. Our back-end runs a scalable closed-form Bayesian inference with only logarithmic time complexity. We apply the framework to build a dense robotic map, including metric-semantic occupancy and traversability layers. Traversability ground truth labels are automatically generated from exteroceptive sensory data in a self-supervised manner. We present extensive experimental results on publicly available datasets and data collected by a three-dimensional bipedal robot platform and show reliable mapping performance in different environments. Finally, we also discuss how the current framework can be extended to incorporate more information, such as friction, signal strength, temperature, and physical quantity concentration using Gaussian map layers. The software for reproducing the presented results or running on customized data is made publicly available. 

Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discretetime, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers.