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Finite-Time Attitude Synchronization with Distributed Discontinuous Protocols ; ; et al in IEEE Transactions on Automatic Control (in press) The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed ... [more ▼] The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper. [less ▲] Detailed reference viewed: 95 (1 UL)Decentralized cooperative tracking subject to motion constraints ; Markdahl, Johan ; et al in Automatica (2018), 96 This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes ... [more ▼] This paper addresses the formation control problem, where three agents are tasked with moving an object cooperatively along a desired trajectory while also adjusting its posture to some desired attitudes, i.e. position and attitude tracking. Two decentralized control laws based on locally available information are proposed. The first control law maintains constant inter-agent distances over time, i.e. the formation of agents moves as a single rigid-body. The second control law relaxes this constraint by only maintaining similarity of the agent formation as a polygon in Euclidean space. [less ▲] Detailed reference viewed: 151 (1 UL)Intrinsic reduced attitude formation with ring inter-agent graph ; Markdahl, Johan ; et al in Automatica (2017), 85 This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle ... [more ▼] This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states. [less ▲] Detailed reference viewed: 80 (0 UL)A geodesic feedback law to decouple the full and reduced attitude Markdahl, Johan ; ; et al in System and Control Letters (2017), 102 This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n−1-sphere. Meanwhile, the full attitude is ... [more ▼] This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n−1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example. [less ▲] Detailed reference viewed: 97 (0 UL)Global and invariant aspects of consensus on the n-sphere Markdahl, Johan ; ; et al in Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems (2016, July) This paper concerns two aspects of the multi- agent consensus problem on the n-sphere. Firstly, it proves that a standard consensus protocol, in a certain sense, yields asymptotical stability on a global ... [more ▼] This paper concerns two aspects of the multi- agent consensus problem on the n-sphere. Firstly, it proves that a standard consensus protocol, in a certain sense, yields asymptotical stability on a global level for a nontrivial class of graph topologies. Secondly, it provides a novel consensus protocol that leaves the centroid of agent states in Rn+1 projected back to the sphere invariant. It hence becomes possible to determine the consensus point as a function of the initial states. Much of the stability analysis has an intuitive geometric appeal since it is based on the symmetries of the n-sphere rather than generic Lyapunov theory. [less ▲] Detailed reference viewed: 103 (7 UL)Exact solutions to a class of feedback systems on SO(n) Markdahl, Johan ; in Automatica (2016), 63 This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on View the MathML source. The closed-loop systems are solved ... [more ▼] This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on View the MathML source. The closed-loop systems are solved exactly for the rotation matrices as explicit functions of time, the initial conditions, and the gain parameters of the control laws. The exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix. Applications of these results are found in model predictive control problems where detailed insight into the transient attitude dynamics is utilized to approximately complete a task of secondary importance. Knowledge of the future trajectory of the states can also be used as an alternative to the zero-order hold in systems where the attitude is sampled at discrete time instances. [less ▲] Detailed reference viewed: 86 (3 UL)Consensus and Formation Control on SE(3) for Switching Topologies Thunberg, Johan ; Goncalves, Jorge ; in Automatica (2016), 66 This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the ... [more ▼] This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it is shown that the proposed control laws can be used for the formation problem. The design is first conducted on the kinematic level, where the velocities are the control laws. Then, for rigid bodies in space, the design is conducted on the dynamic level, where the torques and the forces are the control laws. On the kinematic level, first two control laws are introduced that explicitly use Euclidean transformations, then separate control laws are defined for the rotations and the translations. In the special case of purely rotational motion, the consensus problem is referred to as consensus on SO(3) or attitude synchronization. In this problem, for a broad class of local representations or parameterizations of SO(3), including the Axis–Angle Representation, the Rodrigues Parameters and the Modified Rodrigues Parameters, two types of control laws are presented that look structurally the same for any choice of local representation. For these two control laws we provide conditions on the initial rotations and the connectivity of the graph such that the system reaches consensus on SO(3). Among the contributions of this paper, there are conditions for when exponential rate of convergence occurs. A theorem is provided showing that for any choice of local representation for the rotations, there is a change of coordinates such that the transformed system has a well known structure. [less ▲] Detailed reference viewed: 114 (12 UL)Optimal output consensus for linear systems: a topology free approach Thunberg, Johan ; in Automatica (2016), 68 In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the ... [more ▼] In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the outputs of the agents shall coincide at some given finite time. This is an instance of the rendezvous or finite time consensus problem. We solve this problem without any constraints on the communication topology and provide a solution as an explicit feedback control law for the case when the dynamics of the agents is output controllable. It turns out that the communication graph topology induced by the solution is complete. Based on this solution for the finite time consensus problem, we provide a solution to the case of infinite time horizon. Furthermore, we investigate under what circumstances it is possible to express the controller as a feedback control law of the output instead of the states. [less ▲] Detailed reference viewed: 129 (5 UL) |
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