arXiv subjects

Leonardo J. Colombo

Publications and source records attributed to Leonardo J. Colombo.

31 records · Page 2Linked to original sources

arXiv2022

Learning-Based Fault-Tolerant Control for an Hexarotor with Model Uncertainty

In this paper we present a learning-based tracking controller based on Gaussian processes (GP) for a fault-tolerant hexarotor in a recovery maneuver. In particular, to estimate certain uncertainties that appear in a hexacopter vehicle with the ability to reconfigure its rotors to compensate for failures. The rotors reconfiguration introduces disturbances that make the dynamic model of the vehicle differ from the nominal model. The control algorithm is designed to learn and compensate the amount of modeling uncertainties after a failure in the control allocation reconfiguration by using GP as a learning-based model for the predictions. In particular the presented approach guarantees a probabilistic bounded tracking error with high probability. The performance of the learning-based fault-tolerant controller is evaluated through experimental tests with an hexarotor UAV.

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arXiv2021

Distributed event-triggered flocking control of Lagrangian systems

In this paper, an event-triggered control protocol is developed to investigate flocking control of Lagrangian systems, where event-triggering conditions are proposed to determine when the velocities of the agents are transmitted to their neighbours. In particular, the proposed controller is distributed, since it only depends on the available information of each agent on their own reference frame. In addition, we derive sufficient conditions to avoid Zeno behaviour. Numerical simulations are provided to show the effectiveness of the proposed control law.

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arXiv2021

Learning Rigidity-based Flocking Control with Gaussian Processes

Flocking control of multi-agents system is challenging for agents with partially unknown dynamics. This paper proposes an online learning-based controller to stabilize flocking motion of double-integrator agents with additional unknown nonlinear dynamics by using Gaussian processes (GP). Agents interaction is described by a time-invariant infinitesimally minimally rigid undirected graph. We provide a decentralized control law that exponentially stabilizes the motion of the agents and captures Reynolds boids motion for swarms by using GPs as an online learning-based oracle for the prediction of the unknown dynamics. In particular the presented approach guarantees a probabilistic bounded tracking error with high probability.

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arXiv2021

Geometric Control for Load Transportation with Quadrotor UAVs by Elastic Cables

Groups of unmanned aerial vehicles (UAVs) are increasingly utilized in transportation task as the combined strength allows to increase the maximum payload. However, the resulting mechanical coupling of the UAVs impose new challenges in terms of the tracking control. Thus, we design a geometric trajectory tracking controller for the cooperative task of four quadrotor UAVs carrying and transporting a rigid body, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the position and attitude of the load exponentially converges to a given desired trajectory. We then show that this result leads to an uniformly converging tracking error for the original elastic model under some assumptions. Furthermore, under the presence of unstructured disturbances on the system, we show that the error is ultimately bounded with an arbitrarily small bound. Finally, a simulation illustrates the theoretical results.

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arXiv2021

Variational Obstacle Avoidance with Applications to Interpolation Problems in Hybrid Systems

We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the dynamical equations for extrema in the variational problem, and show the existence of minimizers by using lower-continuity arguments for weak convergence on an infinite-dimensional Hilbert manifold. We then provide conditions under which it is possible to ensure that the extrema will safely avoid a given obstacle within some desired tolerance.

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arXiv2021

Geometric Control of two Quadrotors Carrying a Rigid Rod with Elastic Cables

This paper presents the design of a geometric trajectory tracking controller for the cooperative task of two quadrotor UAVs (unmanned aerial vehicles) carrying and transporting a rigid bar, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the rod exponentially tracks a given desired trajectory for its position and attitude, under some assumptions on initial error. We then show that exponential tracking in the reduced model corresponds to exponential tracking of the original elastic model. We also show that the previously defined control scheme provides uniform ultimate boundedness in the presence of unstructured bounded disturbances.

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arXiv2021

Variational Collision Avoidance on Riemannian Manifolds

This paper studies variational collision avoidance problems for multi-agents systems on complete Riemannian manifolds. That is, we minimize an energy functional, among a set of admissible curves, which depends on an artificial potential function used to avoid collision between the agents. We show the global existence of minimizers to the variational problem and we provide conditions under which it is possible to ensure that agents will avoid collision within some desired tolerance. We also study the problem where trajectories are constrained to have uniform bounds on the derivatives, and derive alternate safety conditions for collision avoidance in terms of these bounds - even in the case where the artificial potential is not sufficiently regular to ensure existence of global minimizers.

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arXiv2020

Structure Preserving Reduced Attitude Control of Gyroscopes

We design a reduced attitude controller for reorienting the spin axis of a gyroscope in a geometric control framework. The proposed controller preserves the inherent gyroscopic stability associated with a spinning axis-symmetric rigid body. The equations of motion are derived in two frames: a non-spinning frame to show the gyroscopic stability, and a body-fixed spinning frame for deriving the controller. The proposed controller is designed such that it retains the gyroscopic stability structure in the closed loop and renders the desired equilibrium almost-globally asymptotically stable. Due to the time-critical nature of the control input, in particular its sensitivity with respect to delays/neglected dynamics, the controller is extended to incorporate the effect of actuator dynamics for practical implementation. Thereafter, a comparison in performance is shown between the proposed controller and a conventional reduced attitude geometric controller with numerical simulation. The controller is validated experimentally on a spinning tricopter.

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arXiv2020

A note on Hybrid Routh reduction for time-dependent Lagrangian systems

This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results for continuous-time systems. We illustrate the applicability of the method using the example of a billiard with moving walls.

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arXiv2020

Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems

We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the distribution which defines the nonholonomic constraints. The problem is studied from a geometric framework. Optimality conditions are determined by the Pontryagin Maximum Principle and also from a variational point of view, which allows the construction of geometric integrators. Examples and numerical simulations are shown to validate the results.

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arXiv2019

Variational collision and obstacle avoidance of multi-agent systems on Riemannian manifolds

In this paper we study a path planning problem from a variational approach to collision and obstacle avoidance for multi-agent systems evolving on a Riemannian manifold. The problem consists of finding non-intersecting trajectories between the agent and prescribed obstacles on the workspace, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the velocity, covariant acceleration and an artificial potential function used to prevent collision with the obstacles and among the agents. We apply the results to examples of a planar rigid body, and collision and obstacle avoidance for agents evolving on a sphere.

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arXiv2019

Motion Feasibility Conditions for Multi-Agent Control Systems on Lie Groups

We study the problem of motion feasibility for multiagent control systems on Lie groups with collision avoidance constraints. We first consider the problem for kinematic left invariant control systems and next, for dynamical control systems given by a left-trivialized Lagrangian function. Solutions of the kinematic problem give rise to linear combinations of the control inputs in a linear subspace annihilating the collision avoidance constraints. In the dynamical problem, motion feasibility conditions are obtained by using techniques from variational calculus on manifolds, given by a set of equations in a vector space, and Lagrange multipliers annihilating the constraint force that prevents deviation of solutions from a constraint submanifold.

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arXiv2014

Lagrangian mechanics on centered semi-direct product

There exists two types of semi-direct products between a Lie group $G$ and a vector space $V$. The left semi-direct product, $G \ltimes V$, can be constructed when $G$ is equipped with a left action on $V$. Similarly, the right semi-direct product, $G \rtimes V$, can be constructed when $G$ is equipped with a right action on $V$. In this paper, we will construct a new type of semi-direct product, $G \Join V$, which can be seen as the `sum' of a right and left semi-direct product. We then parallel existing semi-direct product Euler-Poincaré theory. We find that the group multiplication, the Lie bracket, and the diamond operator can each be seen as a sum of the associated concepts in right and left semi-direct product theory. Finally, we conclude with a toy example and the group of 2-jets of diffeomorphisms above a fixed point. This final example has potential use in the creation of particle methods for problems on diffeomorphism groups.

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