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Control barrier functions (CBFs) offer a powerful tool for enforcing safety specifications in control synthesis. This paper deals with the problem of constructing valid CBFs. Given a second-order system and any desired safety set with…

We apply the method of controlled Lagrangians by potential shaping to Euler--Poincar\'e mechanical systems with broken symmetry. We assume that the configuration space is a general semidirect product Lie group $\mathsf{G} \ltimes V$ with a…

This paper proposes a novel online motion planning approach to robot navigation based on nonlinear model predictive control. Common approaches rely on pure Euclidean optimization parameters. In robot navigation, however, state spaces often…

Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of such systems is commonly invariant to the induced action by…

Neglecting complex aerodynamic effects hinders high-speed yet high-precision multirotor autonomy. In this paper, we present a computationally efficient learning-based model predictive controller that simultaneously optimizes a trajectory…

In order to stabilize nonlinear systems modeled by stochastic differential equations, we design a Fast Exponentially Stable and Safe Neural Controller (FESSNC) for fast learning controllers. Our framework is parameterized by neural…

Autonomous robotic systems heavily rely on environment knowledge to safely navigate. For search & rescue, a flying robot requires robust real-time perception, enabled by complementary sensors. IMU data constrains acceleration and rotation,…

This paper presents a novel method for controlling teams of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level planner that computes optimal state trajectories as…

This paper proposes a unified robust motion controller for the position and force control problems of compliant robot manipulators driven by Series Elastic Actuators (SEAs). It is shown that the dynamic model of the compliant robot includes…

Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities.…

Conventional passivity-based torque controllers for manipulators are typically unconstrained, which can lead to safety violations under external perturbations. In this paper, we employ viability theory to pre-compute safe sets in the…

Evaluating and updating the obstacle avoidance velocity for an autonomous robot in real-time ensures robustness against noise and disturbances. A passive damping controller can obtain the desired motion with a torque-controlled robot, which…

We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…

Lie groups and their actions are ubiquitous in the description of physical systems, and we explore implications in the setting of model order reduction (MOR). We present a novel framework of MOR via Lie groups, called MORLie, in which…

This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie…

This tutorial presents a control-oriented introduction to aided inertial navigation systems using a Lie-group formulation centered on the extended Special Euclidean group SE_2(3). The focus is on developing a clear and…

We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…

For the task of moving a set of indistinguishable agents on a connected graph with unit edge distance to an arbitrary set of goal vertices, free of collisions, we propose a fast distance optimal control algorithm that guides the agents into…

Cartesian impedance control is a type of motion control strategy for robots that improves safety in partially unknown environments by achieving a compliant behavior of the robot with respect to its external forces. This compliant robot…

This paper proposes a novel Taylor-Lagrange Control (TLC) method for nonlinear control systems to ensure the safety and stability through Taylor's theorem with Lagrange remainder. To achieve this, we expand a safety or stability function…