Related papers: The Geometry and Kinematics of the Matrix Lie Grou…
Learning robot motions from demonstration requires models able to specify vector fields for the full robot pose when the task is defined in operational space. Recent advances in reactive motion generation have shown that learning adaptive,…
This paper presents a contact-aided inertial-kinematic floating base estimation for humanoid robots considering an evolution of the state and observations over matrix Lie groups. This is achieved through the application of a geometrically…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
Lie theory is, beyond any doubt, an absolutely essential part of differential geometry. It is therefore necessary to seek its generalization to $\mathbb{Z}$-graded geometry. In particular, it is vital to construct non-trivial and explicit…
Geometry of the state space is known to play a crucial role in many applications of Kalman filters, especially robotics and motion tracking. The Lie group-centric approach is currently very common, although a Riemannian approach has also…
The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of exponential family. Second, it uses gradients which can be…
This paper presents the design and implementation of a Right Invariant Extended Kalman Filter (RIEKF) for estimating the states of the kinematic base of the Surena V humanoid robot. The state representation of the robot is defined on the…
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…
This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of…
Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an…
To fuse information from inertial measurement units (IMU) with other sensors one needs an accurate model for IMU error propagation in terms of position, velocity and orientation, a triplet we call extended pose. In this paper we leverage a…
Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…
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…
This paper considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape…
There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on…
This paper proposes an $SE_2(3)$ based extended Kalman filtering (EKF) framework for the inertial-integrated state estimation problem. The error representation using the straight difference of two vectors in the inertial navigation system…
Camera motion estimation from observed scene features is an important task in image processing to increase the accuracy of many methods, e.g. optical flow and structure-from-motion. Due to the curved geometry of the state space SE(3) and…
The control of free-floating robots requires dealing with several challenges. The motion of such robots evolves on a continuous manifold described by the Special Euclidean Group of dimension 3, known as SE(3). Methods from finite horizon…
We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference…
In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…