his paper addresses the trajectory tracking problem for a quadcopter system under nominal and fault-affected scenarios, the latter case considers stuck actuator(s)). Differential flatness is employed for trajectory generation and control design. The particularity resides in that a full parametrization of the states and inputs is given without any assumptions or simplifications on the quadcopter dynamics. Furthermore, using the properties of flatness and a combination between computed torque control and feedback linearization, a two layer control design is proposed. The tracking performances and stability gurantees are analyzed for nominal and faulty functioning under extensive simulations.
This paper addresses a novel combination between mixed-integer representations and potential field constructions for typical multi-agent marine control problems. First, we prove that for any kind of repulsive functions applied over a function which we denote as sum function, the feasible domain is piece-wise affine (PWA). Next, concepts like hyperplane arrangements together with potential field approaches are used for providing an efficient description of the feasible non-convex domain. This combination offers an original and beneficent computation of control laws under non-convex constraints. Simulation results over a common application of obstacle avoidance, which can be extended for unmanned surface vehicles, prove the effectiveness of the proposed approach.
This paper considers the collision avoidance problem in a multi-agent multi-obstacle framework. The originality in solving this intensively studied problem resides in the proposed geometrical view combined with differential flatness for trajectory generation and B-splines for the flat output parametrization. Using some important properties of these theoretical tools we show that the constraints can be validated at all times. Exact and sub-optimal constructions of the collision avoidance optimization problem are provided. The results are validated through extensive simulations over standard autonomous aerial vehicle dynamics.
One challenging and not extensively studied issue in obstacle avoidance is the corner cutting problem. Avoidance constraints are usually imposed at the sampling time without regards to the intra-sample behavior of the dynamics. This paper improves upon state of the art by describing a multi-obstacle environment via a hyperplane arrangement, provides a piecewise description of the forbidden regions and represents them into a combined mixed integer and predictive control formulation. Furthermore, over-approximation constraints which reduce to strictly binary conditions are discussed in detail. Illustrative proofs of concept, comparisons
with the state of the art and simulation results over a classical multi-obstacle avoidance problem validate the benets of the proposed approach.
This paper addresses the microgrid energy management problem within a coherent framework of control tools based on Mixed-Integer Linear Programming (MILP) and constrained Model Predictive Control (MPC). These help characterize the microgrid components’ dynamics and the overall system control architecture. A fault tolerant strategy is considered in order to ensure the proper amount of energy in the storage devices such that (together with the utility grid) the essential consumer demand is reliably covered. Simulation results on a particular microgrid architecture validate the proposed approach.
This paper addresses some alternatives to classical trajectory generation for an autonomous vehicle which needs to pass through a priori given way-points. Using differential flatness for trajectory generation and B-splines for the flat output parametrization, the current study concentrates on constraint relaxations and on obstacle avoidance conditions. The results are validated through simulations over standard UAV dynamics.
This paper presents an extension of a MPC (Model Predictive Control) approach for microgrid energy management which takes into account electricity costs, power consumption, generation profiles, power
and energy constraints as well as uncertainty due to variations in the environment. The approach is based on a coherent framework of control tools, like mixed-integer programming and soft constrained
MPC, for describing the microgrid components dynamics and the overall system control architecture Fault tolerant strategies are inserted in order to ensure the proper amount of energy in the storage
devices such that (together with the utility grid) the essential consumer demand is always covered. Simulation results on a particular microgrid architecture validate the proposed approach.
This paper addresses the coverage problem for a collection of agents and fixed obstacles (e.g., the “gallery” and the “patrolling” problems). A collection of sufficient conditions over the positions of the agents are provided such that whenever these are verified there is no “blind” region in the feasible space. These conditions are expressed by making use of hyperplane
arrangements which lead to a mixed-integer formulation. Practical applications regarding the coverage problem inside an augmented space with obstacles validate these concepts and
provide an efficient implementation (in terms of computing power).
The current paper addresses the problem of minimizing the computational complexity of optimization problems with non-convex and possibly non-connected feasible region of polyhedral type. Using hyperplane arrangements and Mixed-Integer Programming we provide an efficient description of the feasible region in the solution space. Moreover, we exploit the geometric properties of the hyperplane arrangements and adapt this description in order to provide an efficient solution of the mixed-integer optimization problem. Furthermore, a zonotopic representation of the sets appearing in the problem is considered. The advantages of this representation are highlighted and exploited through proof of concepts illustrations as well as simulation results.
This chapter proposes a distributed approach for the resolution of a multiagent problem under collision and obstacle avoidance conditions. Using hyperplane arrangements and mixed integer programming, we provide an efficient description of the feasible region verifying the avoidance constraints. We exploit geometric properties of hyperplane arrangements and adapt this description to the distributed scheme in order to provide an efficient Model Predictive Control (MPC) solution. Furthermore,we prove constraint validation for a hierarchical ordering of the agents.
This paper is concerned with improvements in constraints handling for mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly not connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a typical control application, the control of multiagent systems using receding horizon optimization techniques, is considered.
This paper is concerned with the improved constraints handling in mixed-integer optimization problems. The novel element is the reduction of the number of binary variables
used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly non-connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a practical implementation, the problem of obstacle avoidance using receding horizon optimization techniques is considered.
The current paper addresses the problem of optimizing a cost function over a non-convex and possibly non-connected feasible region. A classical approach for solving this type of optimization problem is based on Mixed integer technique. The exponential complexity as a function of the number of binary variables used in the problem formulation highlights the importance of reducing them. Previous work which minimize the number of binary variables is revisited and enhanced. Practical limitations of the procedure are discussed and a typical control application, the control of Multi-Agent Systems is exemplified.