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Satisficing Control for Multi-agent Formation Maneuvers
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ren, Wei Beard, Randal W. Curtis, J. Willard |
| Copyright Year | 2002 |
| Abstract | In this paper, robustly satisficing controls based on control Lyapunov functions are applied to multi-agent formation problems. We show that under certain conditions a group of satisficing control laws chosen from the robustly satisficing set can guarantee bounded formation keeping error, finite completion time, and reasonable formation velocity as well as inverse optimality and desirable stability margins. This technique is applied to a group of nonholonomic robots in simulation as a proof of concept. 1 I n t r o d u c t i o n The coordination and control of formations of multiagents have been a topic of interest recently [1, 2, 3] with application to the coordination of multiple robots, UAVs, satellites, aircraft, and spacecraft. While the applications are different, the fundamental approaches to formation control are similiar: the common theme being the coordination of multiple vehicles to accomplish an objective. The motivation for the research of multi-agent formation control results from the following observations. First, in some situations using multiple agents is more feasible and beneficial than using one single agent, e.g. spacecraft inteferometry problems in deep space. Second, the likelihood of success may be improved if multiple agents are used to carry out a mission, e.g. target attacking in a battlefield scenario. Finally, cost and energy efficiency may be maximized if multiple agents can coordinate their movements in a certain way, e.g. multiple aircraft flying in a V-shape formation to maximize fuel efficiency. This paper addresses the issue of multi-agent formation maneuvers by combining the group control Lyapunov function (clf) approach [4] with the recently introduced satisficing paradigm [5]. A central result of this paper is to extend the application of satisficing controls from regulation problems to pointwise time-varying regulation problems, and to provide a group of explicit state-feedback control laws based on clfs (see [6, 7]) for multi-agent formation problems. Following [4] the resulting controls guarantee that the multi-agent system has bounded formation error, finite completion time, and reasonable formation velocity, and that the whole system can reach its final goal eventually. Clf-based satisficing control [5] evolved from the recently introduced notion of satisficing decision theory [8, 9] which can be seen as a formal application of cost-benefit analysis to decision making problems. When combined with the global properties of clfs, satisficing is a powerful design tool which conveniently parameterizes the entire class of continuous control laws which stabilize the closed-loop system with respect to a known clf. Additionally, robust satisficing [5] parameterizes a large class of satisficing controls which have the added benefit of desirable stability margins and which are inverse-optimal. In [5] satisficing is used to provide a group of clfbased state-feedback control laws for arlene nonlinear autonomous systems. Under certain definitions and parameterizations, these control laws are guaranteed to be inverse-optimal with desirable stability margins. However, satisficing controllers are only discussed for regulation problems. Even if tracking problems are reduced to regulation problems the original autonomous system will become nonautonomous, rendering the approach in [5] no longer valid. In [4] clfs are used to define a formation error so that a constrained motion control problem of multiple systerns is converted into a stabilization problem for one single system. Under certain assumptions, a team of formation constrained autonomous agents is guaranteed to maintain a given formation, however explicit control laws which satisfy these assumptions are not given. Also, the formation function is not guaranteed to converge to zero when the team reaches its final goal. This paper is aimed at connecting the satisficing approach with multi-agent formation control problems to simplify controller design as well as guarantee formation maintenance. We extend satisficing to pointwise time-varying regulation problems and show that under certain conditions robustly satisficing controllers can guarantee the assumptions in [4] such that a class of control laws is available for formation control. 2 S a t i s f i c i n g C o n t r o l l e r s As models for each individual agent, we will consider only affine nonlinear systems of the form ic = f (x) + g(x)u, (1) where x E iR '~, f: iR '~ --+ iR '~, g: iR '~ --+ ~ x , ~ and u C IR "~. We will assume throughout the paper tha t f and g are locally Lipschitz functions. A twice continuously differentiable function (C 2) V: IR '~ --+ IR is said to be a control Lyapunov function (clf) for the systern if V is positive definite, radially unbounded, and if infu Vx T ( f + gu) < 0, for all x ~ 0. The basic idea of satisficing is to define two utility functions tha t quantify the benefits and costs of an action. At a state x, the benefits of choosing a control u are given by the "selectablity" function ps(u,x) . Similiarly, at a state x, the costs associated with choosing u are given by the "rejectability" function pr(u,x) . The "satisficing" set is those options for which selectability exceeds rejectability: i.e., Sb(X) = { u : ps(U,x) > ~pr(u,x)} where b(x) is a (possibly state-dependent) parameter tha t can be used to control the size of the set. As in [5], we will associate the notion of selectability with stability, and the notion of rejectability with ins tantaneous cost. In particular, let ps(u, x) = -Vx T ( f + gu), where V is a known clf. Obviously, only stabilizing controls will make p,(u, x) positive. We choose the rejectability criteria to be pr(u,x) = l(x) + uTR(x)u , where R(x) = R(x) T > 0 is a positive definite matrix function whose elements are locally Lipschitz and l: IR '~ -+ IR is a locally Lipschitz non-negative function. For these choices the satisficing set becomes (l(x) + 1 & ( x ) e Vxr(f + > uT t~(x)u) (2) Note if the value of b is too small, Sb might be empty. To ensure tha t the satisficing set is always nonempty we define: t if VxTg _ 0 b(x) A_ -v s, 2vTfq-2V(VTf)2q-IVTgR-lgTV~ otherwise " VT gRl gT V~ (a) From Lemma 5 in [5], we know that for each x ~: 0, __b(x) __ 0, and b > __b(x) implies tha t &(x) # ¢. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ee.byu.edu/~beard/papers/preprints/RenBeardCurtis02.ps |
| Alternate Webpage(s) | http://sites.math.rutgers.edu/~sontag/FTPDIR/02cdc-papers-refs-eds/444_ThA02-5.pdf |
| Alternate Webpage(s) | http://vision.ai.uiuc.edu/~tankh/citations/virtual_structures_AutoRobot1997/Ren_DC2002.pdf |
| Alternate Webpage(s) | http://www.math.rutgers.edu/~sontag/FTP_DIR/02cdc-papers-refs-eds/444_ThA02-5.pdf |
| Alternate Webpage(s) | http://math.rutgers.edu/~sontag/FTPDIR/02cdc-papers-refs-eds/444_ThA02-5.pdf |
| Alternate Webpage(s) | http://www.math.rutgers.edu/~sontag/FTPDIR/02cdc-papers-refs-eds/444_ThA02-5.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Addresses (publication format) Agent-based model Arabic numeral 0 Autonomous robot Autonomous system (Internet) Choose (action) Consensus dynamics Controllers Converge Decision Making Decision theory Design tool Drug vehicle Emoticon Feedback Lyapunov fractal Movement Multi-agent system Nonlinear system Numerical stability Numerous Population Parameter Programming paradigm Robot (device) Satellite Viruses Simulation Tacrine Unmanned aerial vehicle Velocity (software development) adenotonsillectomy benefit |
| Content Type | Text |
| Resource Type | Article |
