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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. 

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. 

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. 

This paper reports on developing an integrated framework for safety-aware informative motion planning suitable for legged robots. The information-gathering planner takes a dense stochastic map of the environment into account, while safety constraints are enforced via Control Barrier Functions (CBFs). The planner is based on the Incrementally-exploring Information Gathering (IIG) algorithm and allows closed-loop kinodynamic node expansion using a Model Predictive Control (MPC) formalism. Robotic exploration and information gathering problems are inherently path-dependent problems. That is, the information collected along a path depends on the state and observation history. As such, motion planning solely based on a modular cost does not lead to suitable plans for exploration. We propose SAFE-IIG, an integrated informative motion planning algorithm that takes into account: 1) a robot’s perceptual field of view via a submodular information function computed over a stochastic map of the environment, 2) a robot’s dynamics and safety constraints via discrete-time CBFs and MPC for closedloop multi-horizon node expansions, and 3) an automatic stopping criterion via setting an information-theoretic planning horizon. The simulation results show that SAFE-IIG can plan a safe and dynamically feasible path while exploring a dense map.