A Control Barrier Function (CBF)-based motion planning algorithm is proposed. The algorithm explores an unknown environment to reach a target point, providing velocity commands to the robot controller module. CBFs, along with a circulation inequality are used to generate safe paths toward the goal while preventing collisions with obstacles. The proposed global navigation scheme is experimentally verified on a quadruped platform to demonstrate safe, collision-free exploration over long distances.

In this paper, we propose an algorithm for computing a smoothed version of the distance between two objects. As opposed to the traditional Euclidean distance between two objects, which may not be differentiable, this smoothed distance is guaranteed to be differentiable. Differentiability is an important property in many applications, in particular in robotics, in which obstacle-avoidance schemes often rely on the derivative/Jacobian of the distance between two objects. We prove mathematical properties of this smoothed distance and of the algorithm for computing it, and show its applicability in robotics by applying it to a second order kinematic control framework, also proposed in this paper. The control framework using smooth distances was successfully implemented on a 7 DOF manipulator.

In this work, we present a methodology to compute an artificial time-varying vector field in$n$dimensions that defines trajectories that converge to and follow a given desired curve. The Euclidean distance function is used to construct the field, which is easily computed from a parametric representation of the curve. The computation of the time feedforward term to compensate for time dependence is such that its norm is limited by the maximum velocity of the curve. This fact allows the normalization of the time-varying vector field such that it has a constant norm without any negative effect for convergence. We present convergence proofs for the proposed normalized time-varying vector field and demonstrate the existence of ultimate bounds in the case bounded disturbances are present. Finally, we show several simulations and experiments with an actual quadrotor to validate our methodology.

The present work focuses on the development of an efficient path controller to guide a fixed-wing UAV (Unmanned Aerial Vehicle) to follow a closed curve and avoid unknown dynamic obstacles. Our strategy is composed of two layers: a top level layer responsible for guidance and a lower level layer responsible for tracking the references given by the top level. To solve the guidance problem, we propose a vector field strategy that switches between two forms: a vector field to converge and circulate the target curve and a vector field to avoid obstacles by circulating the closest one. To make the fixed-wing UAV follow the velocity provided by the guidance vector field we consider a Model Predictive Control scheme. The feedback linearization allows efficient computation of control commands as a linear MPC controller can be employed. Our results are validated in simulations that take into account the 6DOF (Degrees of Freedom) model with constraints of the aircraft, wind disturbance and uncertainties on the measurements.

This article presents a path tracking control strategy for a quadcopter to follow a time varying curve. The control is based on artificial vector fields. The construction of the field is based on a well known technique in the literature. Next, control laws are developed to impose the behavior of the vector field to a second order integrator model. Finally, control laws are developed to impose the dynamics of the controlled second order integrator to a quadcopter model, which assumes the thrust and the angular rates as input commands. Asymptotic convergence of the whole system is proved by showing that the individual systems in cascade connection are input-to-state stable. We also analyze the influence of norm-bounded disturbances in the control inputs to evaluate the robustness of the controller. We show that bounded disturbances originate limited deviations from the target curve. Simulations and a real robot experiment exemplify and validate the developed theory.

This article presents a new kinematic control paradigm for redundant robots based on optimization. The general approach takes into account convex objective functions with inequality constraints and a specific equality constraint resulting from a Lyapunov function, which ensures closed-loop stability by design. Furthermore, we tackle an important particular case by using a convex combination of quadratic and l1-norm objective functions, making possible for the designer to choose different degrees of sparseness and smoothness in the control inputs. We provide a pseudoanalytical solution to this optimization problem and validate the approach by controlling the center of mass of the humanoid robot HOAP3.

This paper presents a guidance vector field strategy to control a fixed-wing UAV (unmanned aerial vehicle)subject to uncertainty in order to converge to and circulate a closed curve in ℝ3. The control system is designed based on a reference model of the airplane with constrained input controls. The law is independent of the vector field's structure, however, some analysis considers a consolidated vector field approach. Asymptotic stability is proven with Lyapunov Theory and ultimate bounds are found when bounded uncertainties are taken into account. The control law is continuous except in the surroundings of the unavoidable field's singularities. A theorem ensures asymptotic convergence when a switch is made. Simulations with a 6 DOF, 12 states realistic aircraft model demonstrate the efficiency of the strategy and its advantages.

This paper addresses the problem of coordinating the motion of multiple fixed-wing Unmanned Aerial Vehicles (UAVs) following closed intersecting curves. We require that each UAV avoid collisions with its teammates without changing its predefined, periodic path. Also, each robot must keep a minimum speed to avoid stall and a maximum speed determined by its physical constraints. The centralized solution presented in this paper is modeled as a Mixed Integer Linear Programming (MILP) problem. The solution to this problem, which maximizes safeness (in the sense of collision avoidance), determines, for each UAV, the start time and the velocity profile over the curve.

Different robotic tasks can be solved by controlling a robot to circulate along curves. These include, for example, border inspection and surveillance, multirobot manipulation, and pattern generation. In a previous, work we have proposed a vector field approach for robot convergence and circulation along time-varying curves embedded in N-dimensional spaces. In the present work we instantiate this approach for three-dimensional spaces and, for the first time, show the efficacy of this method to control actual robots. Besides new theoretical analysis when constant speed control is applied, we present experimental results with aerial (quadrotors) and ground (differential-driven) robot.

This paper presents a methodology for computation of artificial vector fields that allows a robot to converge to and circulate around generic curves specified in$n$-dimensional spaces. These vector fields may be directly applied to solve several robot-navigation problems such as border monitoring, surveillance, target tracking, and multirobot pattern generation, with special application to fixed-wing aerial robots, which must keep a positive forward velocity and cannot converge to a single point. Unlike previous solutions found in the literature, the approach is based on fully continuous vector fields and is generalized to time-varying curves defined in$n$-dimensional spaces. We provide mathematical proofs and present simulation and experimental results that illustrate the applicability of the proposed approach. We also present a methodology for construction of the target curve based on a given set of its samples.