Showing papers by "Joaquin Carrasco published in 2020"

Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning

Abstract: Autonomous exploration is an important application of multi-vehicle systems, where a team of networked robots are coordinated to explore an unknown environment collaboratively. This technique has earned significant research interest due to its usefulness in search and rescue, fault detection and monitoring, localization and mapping, etc. In this paper, a novel cooperative exploration strategy is proposed for multiple mobile robots, which reduces the overall task completion time and energy costs compared to conventional methods. To efficiently navigate the networked robots during the collaborative tasks, a hierarchical control architecture is designed which contains a high-level decision making layer and a low-level target tracking layer. The proposed cooperative exploration approach is developed using dynamic Voronoi partitions, which minimizes duplicated exploration areas by assigning different target locations to individual robots. To deal with sudden obstacles in the unknown environment, an integrated deep reinforcement learning based collision avoidance algorithm is then proposed, which enables the control policy to learn from human demonstration data and thus improve the learning speed and performance. Finally, simulation and experimental results are provided to demonstrate the effectiveness of the proposed scheme.

Convex Searches for Discrete-Time Zames–Falb Multipliers

Abstract: In this article, we develop and analyze convex searches for Zames–Falb multipliers. We present two different approaches: infinite impulse response (IIR) and finite impulse response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large-order FIR multiplier. We show that searches in discrete time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell _{2}$ -stability results in the literature for slope-restricted nonlinearities. In particular, we establish the equivalence between the state-of-the-art Lyapunov results for slope-restricted nonlinearities and a subset of the FIR multipliers. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.

Duality bounds for discrete-time Zames-Falb multipliers

Abstract: We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex.

Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture

Abstract: This paper considers the Lurye system of a discrete-time, linear time-invariant plant in negative feedback with a nonlinearity. Both monotone and slope-restricted nonlinearities are considered. The main result is a procedure to construct destabilizing nonlinearities for the Lurye system. If the plant satisfies a certain phase condition then a monotone nonlinearity can be constructed so that the Lurye system has a non-trivial periodic cycle. Several examples are provided to demonstrate the construction. This represents a contribution for absolute stability analysis since the constructed nonlinearity provides a less conservative upper bound than existing bounds in the literature.

Zames–Falb multipliers for convergence rate: motivating example and convex searches

Abstract: The bound of convergence rates for discrete-time Lurye (sometimes written Lur'e) systems has recently attracted much attention. The contributions of this technical note are twofold. Firstly, we sho...

A Comparative Study for Obstacle Avoidance Inverse Kinematics: Null-Space Based vs. Optimisation-Based

Abstract: Obstacle avoidance for robotic manipulators has attracted much attention in robotics literature, and many algorithms have been developed. In this paper, two algorithms are explored which perform obstacle avoidance within the inverse kinematics calculation process. The first algorithm applies a velocity to the null-space of the manipulator’s Jacobian matrix which directs the manipulator away from obstacles. The second algorithm uses an optimisation-based approach to calculate joint positions which incorporates constraints to prevent the manipulator from violating obstacle boundaries. Applying obstacle avoidance at the inverse kinematics level of the control process is particularly applicable to teleoperation and allows the robotic manipulator to react to obstacles at a faster rate without involving a path planner which operates on a slower cycle time. The two algorithms were implemented for a direct comparison in terms of obstacle avoidance capability and processing times. It was found that the processing time of the null-space method was substantially quicker than the optimisation-based algorithm. However, the null-space method did not guarantee collision avoidance which may not be suitable for safety critical applications without supervision.

Multipliers for nonlinearities with monotone bounds

Abstract: We consider Lurye (sometimes written Lur'e) systems whose nonlinear operator is characterised by a possibly multivalued nonlinearity that is bounded above and below by monotone functions. Stability can be established using a sub-class of the Zames-Falb multipliers. The result generalises similar approaches in the literature. Appropriate multipliers can be found using convex searches. Because the multipliers can be used for multivalued nonlinearities they can be applied after loop transformation. We illustrate the power of the new mutlipliers with two examples, one in continuous time and one in discrete time: in the first the approach is shown to outperform available stability tests in the literature; in the second we focus on the special case for asymmetric saturation with important consequences for systems with non-zero steady state exogenous signals.