This paper presents a generalization of the Compressed Extended Kalman Filter (CEKF) by introducing the definition of the compressed operation for Bayesian estimation processes and the definition of the Generalized Compressed Kalman Filter (GCKF). The GCKF extends the original definition of the CEKF, formerly introduced for treating a family of estimation problems, such as the Simultaneous Localization and Mapping (SLAM). The new proposed approach, the GCKF, is capable of treating problems that are more general than those of the original CEKF, such as estimation processes that involve certain stochastic Partial Differential Equation (SPDE) models. In addition to solving the SLAM and multi-agent SLAM problem in an efficient way, the GCKF can be applied to more general cases. As a proof of the capabilities of the new method for solving practical estimation problems, a multi-agent SLAM process is presented in the experimental section of this paper.

Legged robots may become unstable when subjected to unexpected disturbances such as external pushes and environmental irregularities mostly while moving on natural terrains. To enhance the mobility performance, legged robots should be able to keep or restore their balanced configuration when a sudden disturbance is exerted. The aim of this article is to design a controller for a quadruped robot to restore its balanced configuration despite exerting external pushes. This is achieved based on developing a full-dynamics model of the robot moving over even and uneven terrains. The proposed controller is based on a PD module which calculates the required accelerations for restoring the robot equilibrium. However, these accelerations may make the robot unstable and also cause the slippage of stance feet. Therefore, an optimization algorithm is used to compute the maximum admissible accelerations. The constraints of the optimization problem are the conditions which guarantee the robot stability and the stance feet slippage avoidance. The optimization algorithm is transformed into a linear constrained least-squares problem to be solved in real-time. The main contributions of this article are the development of a push recovery algorithm for quadruped robots and also the introduction of an appropriate condition which guarantees the stability of the robot even on uneven terrains. This stability condition is developed based on a full-dynamics model of the robot. The proposed algorithm is applied on an 18-DOF quadruped robot when the robot is standing over both even and uneven terrains. The obtained results show that the robot can successfully restore its balanced configuration by precise adjustment of the position and orientation of its main body while a massive external disturbance is exerted.

This paper proposes a leader following formation tracking controller for multiple underactuated underwater vehicles (UUVs) which move in three dimensional space. In order to avoid the derivative of the virtual control signals, a control method based on filter backstepping is proposed. The method can significantly simplify the design process of the backstepping controller through the use of a filter rather than the analytic derivation directly to the virtual control variable. Furthermore, the influence of measurement noise is obviously weakened. The stability of the formation system of multiple UUVs has been proved based on Lyapunov stability theory. Simulation results illustrate that the designed controller can track a three-dimensional formation trajectory accurately.

This paper studies bifurcations in the solution structure of an optimal control problem for mobile robotic formation control. In particular, this paper studies a group of mobile robots operating in a two-dimensional environment. Each robot has a predefined initial state and final state and we compute an optimal path between the two states for every robot. The path is optimized with respect to two factors, the control effort and the deviation from a desired “formation,” and a bifurcation parameter gives the relative weight given to each factor. Using an asymptotic analysis, we show that for small values of the bifurcation parameter (corresponding to heavily weighting the control effort) a single unique solution is expected, and that as the bifurcation parameter becomes large (corresponding to heavily weighting maintaining the formation) a large number of solutions is expected. Between the asymptotic extremes, a numerical investigation indicates a solution bifurcation structure with a cascade of increasing numbers of solutions, reminiscent, but not the same as, period-doubling bifurcations leading to chaos in dynamical systems. Furthermore, we show that if the system is symmetric, the bifurcation structure possesses symmetries, and also present a symmetry-breaking example of a non-holonomic system. Knowledge and understanding of the existence and structure of bifurcations in the solutions of this type of formation control problem are important for robotics engineers because common optimization approaches based on gradient-descent are only likely to converge to the single nearest solution, and a more global study provides a deeper and more comprehensive understanding of the nature of this important problem in robotics.

Light-weight manipulators are used in industrial tasks mounted on mobile platforms to improve flexibility. However, such mountings introduce compliance affecting the tasks. This work deals with such scenarios by designing a controller that also takes into account compliant environments. The controller allows the tracking of a target force using the estimation of the environment stiffness (EKF) and the estimation of the base position (KF), compensating the robot base deformation. The closed-loop stability has been analyzed. Observers and the control law have been validated in experiments. An assembly task is considered with a standard industrial non-actuated mobile platform. Control laws with and without base compensation are compared.

This paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

In the real practice of multi-AUV (Autonomous Underwater Vehicle) cooperative systems, tasks or malfunctions will change the topology. The process of mutative topology structure will affect the reliability of multi-AUV cooperative system. The interactive Markov chains model, which is an intercurrent model of functional action and capability index, is selected to reflect the reliability of topology-changed multi-AUV cooperative systems. In this model, multi-AUV cooperative systems are described by the conception—“Action”. The concept of “action transfer” is used to describe the topology-changed multi-AUV cooperative system, and model checking is used to solve the interactive Markov chains, giving the probability of reliability within a certain time for the system. The result shows that the method proposed in this paper has a practical value.

This work presents a novel command strategy developed to improve operator performance and minimize difficulties in teleoperation tasks for mobile-manipulator systems with a holonomic base. Aimed specifically at novice operators, virtual fixtures are introduced as a means to minimize collisions and assist in navigation. Using the 6-degree-of-freedom (DOF) Omnibot mobile-manipulator system (MMS), a command strategy is implemented such that the operator need only control a 3-DOF haptic joystick to achieve full control of the Omnibot MMS. The command strategy is used to coordinate control between the arm and the base of the system, prevent collisions with known obstacles, and alert the operator of proximity to those obstacles with haptic forces. Through experimental testing it is shown that operator performance improved with the use of virtual fixtures.

In Eq. (22), the x symbol was incorrectly represented by an @ symbol, therefore the equation should correctly read as

\begin{eqnarray*} \dot x &=& {f_v}(x) + {g_v}(x)u,\\ {y_v} &=& y_v^a(x) - y_v^d(x). \end{eqnarray*}