Consistent localization of cooperative multi-robot systems during navigation presents substantial challenges. This paper proposes a fault-tolerant, multi-modal localization framework for multi-robot systems on matrix Lie groups. We introduce novel stochastic operations to perform composition, differencing, inversion, averaging, and fusion of correlated and non-correlated estimates on Lie groups, enabling pseudo-pose construction for filter updates. The method integrates a combination of proprioceptive and exteroceptive measurements from inertial, velocity, and pose (pseudo-pose) sensors on each robot in an Extended Kalman Filter (EKF) framework. The prediction step is conducted on the Lie group$\mathbb {SE}_{2}(3) \times \mathbb {R}^{3} \times \mathbb {R}^{3}$, where each robot's pose, velocity, and inertial measurement biases are propagated. The proposed framework uses body velocity, relative pose measurements from fiducial markers, and inter-robot communication to provide scalable EKF update across the network on the Lie group$\mathbb {SE}(3) \times \mathbb {R}^{3}$. A fault detection module is implemented, allowing the integration of only reliable pseudo-pose measurements from fiducial markers. We demonstrate the effectiveness of the method through experiments with a network of wheeled mobile robots equipped with inertial measurement units, wheel odometry, and ArUco markers. The comparison results highlight the proposed method's real-time performance, superior efficiency, reliability, and scalability in multi-robot localization, making it well-suited for large-scale robotic systems.

In this paper, we investigate the motion of wheeled mobile robots on rough terrains modeled as noisy nonholonomic constraints. Such constraints are the natural extension of ideal nonholonomic constraints when the Stratonovich process is directly introduced in the constraint equations. The resulting stochastic model can capture motion on rough surfaces, random deformation in the wheel-ground contact, or stochastic loss/gain of traction. We study a differential robot with ideal noisy and affine noisy constraints, where each case models a certain aspect of motion on rough terrains. We then investigate their corresponding stochastic dynamics and the propagation of mean and covariance through Monte-Carlo simulations. The proposed model for roving rough terrains has the potential to serve as the stochastic model employed in model-based motion planning, pose estimation, and control of rover systems. The main challenge will be dealing with the nonlinear appearance of the noise and its feedback in the equations of motion.

It has been long known that the Euler–Lagrange dynamical equations of fixed-base manipulators with single-degree-of-freedom joints can be formulated on Lie groups following exponential joint parameterizations. Whereas, dynamics of symmetric vehicles can be captured using the Euler–Poincaré equations on Lie groups, with no need to choose any local parameterization. We utilize a combined form of these two geometric approaches called the Lagrange–Poincaré Equations (LPE) to develop a singularity-free Lagrangian formalism for the dynamics of vehicle-manipulator systems. We consider vehicles whose configuration manifolds are Lie subgroups of the special Euclidean group, encompassing arbitrary base vehicle motions corresponding to, e.g., ball, planar, or free joints. We revisit the Lagrange-d'Alembert principle for systems on principal bundles to derive the LPE for vehicle-manipulators with possibly symmetry-breaking externally applied wrenches. These equations effectively separate the external (locked-arm system) and internal dynamics (arm's motion) by introducing a block-diagonalized inertia matrix. We then incorporate the exponential parameterization of manipulators to explicitly formulate the reduced dynamics on Lie groups. The resulting equations are in matrix form and can be immediately implemented in simulations and model-based control strategies. The geometrical significance of the proposed formalism is further demonstrated via the step-by-step presentation of a case study.

Current dynamical models of Cosserat rods often use the finite element method limited by computational efficiency or the finite difference method in a Cartesian framework with a compromise to accuracy. We employ the finite difference method in a geometric framework to develop solutions that are both computationally efficient and accurate. A numerical study is conducted on various backward-differentiation discretization and Runge-Kutta-Munthe-Kaas integration schemes, focusing on their accuracy and computational efficiency. Case studies are conducted on a single-degree-of-freedom joint actuated Cosserat rod to mitigate additional sources of undesired error from the numerical analysis, e.g. multi-body interactions, moving base dynamics, etc. The proposed geometric integrators are demonstrated to improve solution accuracy compared to the published finite difference models. The presented solution is parameterization-free and also computationally efficient with the potential for use in real-time applications, e.g., model-based control of soft manipulators.

We present a full-pose end-effector control approach on Lie groups for free-floating space manipulators with non-zero momentum while tracking a moving target during proximity operations. We model space-manipulators as open-chain multi-body systems with 1-degree-of-freedom joints where the configuration space of the spacecraft is isomorphic to the Special Euclidean group SE(3). We formulate the dynamics of the spacecraft-manipulator via the Lagrange-Poincare equations and the dynamics of its target via Euler-Poincare equations to avoid kinematic singularities associated with parametrization of their poses. This model reduces the phase space of the space-manipulator by exploiting its inherent independence of the spacecraft's pose. We consider the full pose of the end-effector relative to the target as the system output, which transforms the output-tracking control problem into an output-regulation problem. To avoid parametrization singularities of this output, we perform feedback linearization on the matrix Lie group SE (3) in the reduced phase space of the space-manipulator. We then propose a feedback/feedforward proportional-integral-derivative workspace controller, based on coordinate-free pose and velocity error functions defined on the matrix Lie group associated with the target's relative pose. We provide analytical proof of the almost-global stability of the presented controller when regulating the end-effector's pose relative to the target towards identity.

This paper discusses a practical approach to the concurrent synthesis of robot manipulators, which is based on the alternative design methodology of linguistic mechatronics (LM) as well as the utilization of a modular robotic hardware-in-the-loop simulation (RHILS) platform. The RHILS platform involves physical joint modules and the control unit to reduce modeling complexities while taking into account various physical phenomena. The LM methodology simplifies the multi-objective constrained optimization problem into a single-objective unconstrained formulation and also brings subjective notions of design into the scope. The new approach is applied to redesigning kinematic, dynamic and control parameters of an industrial manipulator.