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.

This paper proposes a hybrid control approach to task priority based mobile manipulation. More specifically, it uses a hybrid systems framework to address the problem of end-effector path following for a manipulator attached to a nonholonomic mobile platform where the joints are subject to constraints and the inputs signals are required to be bounded. A switched control strategy allows the robot to avoid infeasible and singular joint configurations while executing a bounded pseudo-inverse based feedback control law. The resulting closed loop system stabilizes the desired path, has a dwell time in each mode, and only switches a finite number of times.

This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using only relative attitude information. Under both undirected and directed ring inter-agent graph, it is shown that when reversing the sign of a classic consensus control, different formations depending on the parity of the group size are achieved asymptotically. Specifically, the reduced attitudes converge to a pair of antipodal points with even number of agents, and distribute uniformly on a great circle with odd number of agents. To show the effectiveness of the proposed control law, illustrative examples are provided.

This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on SO(n). 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.

This paper proposes a hybrid control algorithm for mobile manipulation subject to joint-space constraints. More specifically, we consider the problem of making the end-effector of a planar manipulator attached to a nonholonomic mobile platform reach a set-point or equivalently follow a given path in workspace by means of kinematic actuation. A switched control strategy allows the robot to avoid singular joint configurations and execute a pseudo-inverse based feedback using bounded and continuous control signals. The switching scheme is also utilized to maintain feasible joint configurations. Numerical examples provide an intuitive understanding of the algorithm's workings.

This paper provides analytical solutions to the closed loop system kinematics for a class of almost globally asymptotically stable feedback laws on SO(n). The resulting closed loop kinematics are solved for the respective matrices as functions of time, the initial conditions and the gain parameters of the control laws. The analytical solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix. We consider an application of these results towards model predictive control where the transient phase of the system is utilized to attempt to complete a task of secondary importance by choosing the gain parameters as functions of time and the initial conditions.

This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples.

This paper considers a tracking problem for three manipulators grasping a rigid object. The control objective is to coordinate the movements of the manipulators using local information in order to align the object attitude with a desired rest attitude and the object position with a time parameterized reference trajectory. The object rigidity is modelled as a constraint on the motion of the end-effectors saying that the distance between any pair of end-effectors must be constant in time. The control law consists of a rotational part and a translational part. The translational part also incorporates a linear observer of the reference trajectory. We prove stability and illustrate the system dynamics by simulation.

This paper proposes a switched control algorithm for distributed cooperative manipulation of rigid bodies in a planar setting. More specifically, we consider the problem of making a grasped object follow a desired position and orientation path. The system contains N robots, possibly of heterogeneous designs, each of which consists of a manipulator arm and a nonholonomic mobile platform. Control is based on local information, is carried out on a kinematic level and partly utilizes inverse kinematics. We use Lyapunov-like arguments to prove that the algorithm is almost globally stable and also show that its parameters can be chosen so that any input saturation level is met. The time between certain switches is proved to be bounded below, and the system is shown to be free of any Zeno behavior.

This paper proposes a local information based control law in order to solve the planar manipulation problem of rotating a grasped rigid object to a desired orientation using multiple mobile manipulators. We adopt a multi-agent systems theory approach and assume that: (i) the manipulators (agents) are capable of sensing the relative position to their neighbors at discrete time instances, (ii) neighboring agents may exchange information at discrete time instances, and (iii) the communication topology is connected. Control of the manipulators is carried out at a kinematic level in continuous time and utilizes inverse kinematics. The mobile platforms are assigned trajectory tracking tasks that adjust the positions of the manipulator bases in order to avoid singular arm configurations. Our main result concerns the stability of the proposed control law.