On-orbit assembly using superquadric potential fields

The autonomous on-orbit assembly of a large space structure is presented using a method based on superquadric artificial potential fields. The final configuration of the elements which form the structure is represented as the minimum of some attractive potential field. Each element of the structure is then considered as presenting an obstacle to the others using a superquadric potential field attached to the body axes of the element. A controller is developed which ensures that the global potential field decreases monotonically during the assembly process. An error quaternion representation is used to define both the attractive and superquadric obstacle potentials allowing the final configuration of the elements to be defined through both relative position and orientation. Through the use of superquadric potentials, a wide range of geometric objects can be represented using a common formalism, while collision avoidance can make use of both translational and rotation maneuvers to reduce total maneuver cost for the assembly process

Stabilizing and maneuvering angle rigid multi-agent formations with double-integrator agent dynamics

This paper studies formation stabilization and maneuvering of mobile agents governed by double-integrator dynamics. The desired formation is described by a set of triple-agent angles. A carefully chosen such set of angle constraints guarantees that the desired formation is angle rigid. To achieve the desired angle rigid formation, a stabilization control law is proposed using only local velocity and direction measurements. We show that the closed-loop dynamics of the formation, when each agent is modeled by a double-integrator, are closely related to the corresponding one in single-integrator agent dynamics. Sufficient conditions are constructed to guarantee the closed-loop stability for identical and distinct velocity damping gains, respectively. To guide an angle rigid formation to move with the desired translational velocity, orientation and scale, formation maneuvering laws are then proposed. Simulation examples are also provided to validate the results

Triangular Formation Maneuver Using Designed Mismatched Angles

This paper investigates the problem of triangular formation maneuver control for mobile 3-agent systems with bearing measurements. Different from controlling rigid formations' maneuvering by introducing a pair of mismatches per distance constraint, we introduce a pair of designed- mismatches per angle constraint which leads to the desired triangular formation shape. Considering that for the control of triangular formations with angle constraints, each agent aims at maintaining its own interior angle, to realize the formation maneuver control we design the mismatches into each agent's own desired interior angle. Two types of designed-mismatch are investigated: time-varying case and constant case. For the time-varying case, under the assumption that each agent can additionally measure the relative position from itself to the formation centroid, the triangular formation maneuver control algorithm is designed such that the desired maneuvering in terms of translation, rotation, and scaling can be realized. For the constant case, under the constraint that the desired triangular shape is known only once for the mismatch design, the triangular formation maneuver control algorithm is also proposed, and the angle dynamics are derived by using the dot product of two bearing vectors. Finally, simulation examples demonstrate the effectiveness of the theoretical results

Distributed scaling control of rigid formations

Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by introducing distributed parameters to the prescribed inter-distances we are able to manipulate the steady-state motion of the formation. This manipulation is in the form of inducing simultaneously the combination of constant translational and angular velocities and a controlled scaling of the rigid formation. While the computation of the distributed parameters for the translational and angular velocities is based on the well-known graph rigidity theory, the parameters responsible for the scaling are based on some recent findings in bearing rigidity theory. We carry out the stability analysis of the modified gradient system and simulations in order to validate the main result.Comment: 6 pages In proceedings 55th Conference on Decision and Control, year 201

Mobile Formation Coordination and Tracking Control for Multiple Non-holonomic Vehicles

This paper addresses forward motion control for trajectory tracking and mobile formation coordination for a group of non-holonomic vehicles on SE(2). Firstly, by constructing an intermediate attitude variable which involves vehicles' position information and desired attitude, the translational and rotational control inputs are designed in two stages to solve the trajectory tracking problem. Secondly, the coordination relationships of relative positions and headings are explored thoroughly for a group of non-holonomic vehicles to maintain a mobile formation with rigid body motion constraints. We prove that, except for the cases of parallel formation and translational straight line formation, a mobile formation with strict rigid-body motion can be achieved if and only if the ratios of linear speed to angular speed for each individual vehicle are constants. Motion properties for mobile formation with weak rigid-body motion are also demonstrated. Thereafter, based on the proposed trajectory tracking approach, a distributed mobile formation control law is designed under a directed tree graph. The performance of the proposed controllers is validated by both numerical simulations and experiments

Maneuvering formations of mobile agents using designed mismatched angles

This paper investigates how to maneuver a planar formation of mobile agents using designed mismatched angles. The desired formation shape is specified by a set of interior angle constraints. To realize the maneuver of translation, rotation and scaling of the formation as a whole, we intentionally force the agents to maintain mismatched desired angles by introducing a pair of mismatch parameters for each angle constraint. To allow different information requirements in the design and implementation stages, we consider both measurement-dependent and 10 measurement-independent mismatches. Starting from a triangular formation, we consider generically angle rigid formations that can be constructed from the triangular formation by adding new agents in sequence, each having two angle constraints associated with some existing three agents. The control law for each newly added agent arises naturally from the angle constraints and makes full use of the angle mismatch parameters. We show that the control can effectively stabilize the formations while simultaneously realizing maneuvering. Simulations are conducted to validate the theoretical results

Taming mismatches in inter-agent distances for the formation-motion control of second-order agents

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.Comment: 14 pages, conditionally accepted in Automatic Control, IEEE Transactions o