Autonomous collision avoidance for wheeled mobile robots using a differential game approach

Mylvaganam, Thulasi; Sassano, Mario

doi:10.1016/j.ejcon.2017.11.005

Cited by 43 publications

(41 citation statements)

References 18 publications

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“…An approach similar to potential fields involves using the gradient of a Lyapunov function, which implicitly takes into account the possibility of collisions. Such control laws have been constructed using a differential game approach [127], [128] and simultaneously solve a greedy optimization problem. The difficulty lies in solving the optimal control problem in the presence of nonlinearities and local communication.…”

Section: Collision Avoidance and Collision-free Motionsmentioning

confidence: 99%

A Survey on Aerial Swarm Robotics

et al. 2018

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Abstract-The use of aerial swarms to solve real-world problems has been increasing steadily, accompanied by falling prices and improving performance of communication, sensing, and processing hardware. The commoditization of hardware has reduced unit costs, thereby lowering the barriers to entry to the field of aerial swarm robotics. A key enabling technology for swarms is the family of algorithms that allow the individual members of the swarm to communicate and allocate tasks amongst themselves, plan their trajectories, and coordinate their flight in such a way that the overall objectives of the swarm are achieved efficiently. These algorithms, often organized in a hierarchical fashion, endow the swarm with autonomy at every level, and the role of a human operator can be reduced, in principle, to interactions at a higher level without direct intervention. This technology depends on the clever and innovative application of theoretical tools from control and estimation. This paper reviews the state of the art of these theoretical tools, specifically focusing on how they have been developed for, and applied to, aerial swarms. Aerial swarms differ from swarms of ground-based vehicles in two respects: they operate in a three-dimensional (3-D) space, and the dynamics of individual vehicles adds an extra layer of complexity. We review dynamic modeling and conditions for stability and controllability that are essential in order to achieve cooperative flight and distributed sensing. The main sections of the paper focus on major results covering trajectory generation, task allocation, adversarial control, distributed sensing, monitoring, and mapping. Wherever possible, we indicate how the physics and subsystem technologies of aerial robots are brought to bear on these individual areas.

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Section: Collision Avoidance and Collision-free Motionsmentioning

confidence: 99%

A Survey on Aerial Swarm Robotics

et al. 2018

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“…The control design methodologies presented in this paper have been applied to a variety of problems, such as robotic systems in Sassano and Astolfi (2012), mechanical systems in Passenbrunner, Sassano, and del Re (2011); Sassano and Astolfi (2011), Lotka-Volterra models arising in biological systems in Mylvaganam et al (2015) and power systems in Mylvaganam and Astolfi (2015a). Notably, the results presented in Sections 3 and 4 have been applied to control problems related to multi-agent systems (MAS), including coverage control in Astolfi (2012, 2014), collision avoidance in Mylvaganam and Sassano (2018); Mylvaganam, Sassano, and Astolfi (2017) and formation control Mylvaganam and Astolfi (2015b). In this section we focus on MAS as one possible application of the control design machinery considered in this paper.…”

Section: Application To Multi-agent Collision Avoidancementioning

confidence: 99%

“…In this section we focus on MAS as one possible application of the control design machinery considered in this paper. In particular, as in Mylvaganam and Sassano (2018); , we tackle the so-called multi-agent collision avoidance problem and its solution based on a game theoretic framework. Exploiting Theorem 4.1 the multi-agent collision avoidance problem is solved with local performance guarantees, subject to simple and easily satisfied assumptions.…”

Section: Application To Multi-agent Collision Avoidancementioning

confidence: 99%

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An algebraic approach to dynamic optimisation of nonlinear systems: a survey and some new results

Sassano¹,

Mylvaganam

Astolfi

2018

Journal of Control and Decision

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Dynamic optimisation, with a particular focus on optimal control and nonzero-sum differential games, is considered. For nonlinear systems solutions sought via the dynamic programming strategy are inevitably characterised by partial differential equations (PDEs) which are often difficult to solve. A detailed overview of a control design framework which enables the systematic construction of approximate solutions for optimal control problems and differential games without requiring the explicit solution of any PDE is provided along with a novel design of a nonlinear control gain aimed at improving the 'level of approximation' achieved. Multi-agent systems are considered as a possible application of the theory.

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“…In this paper, we follow the approach of [3] and provide an alternative solution for the problem of local disturbance attenuation with internal stability which is characterised by algebraic equations in place of PDEs and which relies on the immersion of the underlying nonlinear dynamics into an auxiliary (extended) system. These algebraic equations are similar in spirit to the so-called alge-braicP solutions introduced in [9]- [11] and utilised in [12], [13] in the context of optimal control and differential games. The approach enables the systematic construction of dynamic output feedbacks which solve -without approximation -the problem of local disturbance attenuation with internal stability.…”

Section: Introductionmentioning

confidence: 97%

Disturbance Attenuation by Measurement Feedback in Nonlinear Systems via Immersion and Algebraic Conditions

Mylvaganam

Sassano

2020

IEEE Trans. Automat. Contr.

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In this paper we consider the problem of disturbance attenuation with internal stability for nonlinear, input-affine systems via measurement feedback. The solution to the above problem has been provided, three decades ago, in terms of the solution to a system of coupled nonlinear, first-order partial differential equations (PDEs). As a consequence, despite the rather elegant characterization of the solution, the presence of PDEs renders the control design synthesis almost infeasible in practice. Therefore, to circumvent such a computational bottleneck , in this paper we provide a novel characterization of the exact solution to the problem that does not hinge upon the explicit computation of the solution to any PDE. The result is achieved by considering the immersion of the nonlinear dynamics into an extended system for which locally positive definite functions solving the required PDEs may be directly provided in closed-form by relying only on the solutions to Riccati-like, state-dependent, algebraic matrix equations.

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Autonomous collision avoidance for wheeled mobile robots using a differential game approach

Cited by 43 publications

References 18 publications

A Survey on Aerial Swarm Robotics

A Survey on Aerial Swarm Robotics

An algebraic approach to dynamic optimisation of nonlinear systems: a survey and some new results

Disturbance Attenuation by Measurement Feedback in Nonlinear Systems via Immersion and Algebraic Conditions

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