In robotics, path planning and trajectory optimization are usually performed separately to optimize the path from the given starting point to the ending point in the presence of obstacles. In this paper, path planning and trajectory optimization for robotic manipulators are solved simultaneously by a newly developed methodology called Discrete Mechanics and Optimal Control (DMOC). In DMOC, the Lagrange–d'Alembert equation is discretized directly unlike the conventional variational optimization method in which first the Euler–Lagrange equations are derived and then discretization takes place. In this newly developed method, the constraints for optimization of a desired objective function are the forced discrete Euler–Lagrange equations. In this paper, DMOC is used for simultaneous path planning and trajectory optimization for robotic manipulators in the presence of known static obstacles. Two numerical examples, applied on a DELTA parallel robot, are discussed to show the applicability of this new methodology. The optimal results obtained from DMOC are compared with the other state-of-the-art techniques. The difficulties and problems associated in using the DMOC for Parallel Kinematic Machine (PKM) are also discussed in this paper.

We show that the diameter diam(Gn ) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that

$$P(\D(G_n)\in(n^{1/4-\e},n^{1/4+\e}))\geq 1-\exp(-n^{c\e})$$

Control of rigid–flexible multi-body systems in space, during cooperative manipulation tasks, is studied in this paper. During such tasks, flexible members such as solar panels may vibrate. These vibrations in turn can lead to oscillatory disturbing forces on other subsystems, and consequently may produce significant errors in the position of operating end-effectors of cooperative arms. Therefore, to design and implement efficient model-based controllers for such complicated nonlinear systems, deriving an accurate dynamics model is required. On the other hand, due to practical limitations and real-time implementation, such models should demand fairly low computational complexity. In this paper, a precise dynamics model is derived by virtually partitioning the system into two rigid and flexible portions. These two portions will be assembled together to generate a proper model for controller design. Then, an adaptive hybrid suppression control (AHSC) algorithm is developed based on an appropriate variation rule of a virtual damping parameter. Finally, as a practical case study a space free-flying robot (SFFR) with flexible appendages is considered to move an object along a desired path through accurate force exertion by several cooperative end-effectors. This system includes a main rigid body equipped with thrusters, two solar panels, and two cooperative manipulators. The system also includes a third and fourth arm that act as a communication antenna and a photo capturing camera, respectively. The maneuver is deliberately planned such that flexible modes of solar panels get stimulated due to arms motion, while obtained results reveal the merits of proposed controller as will be discussed.

We present the design, control, and human–machine interface of a series elastic holonomic mobile platform, AssistOn-Mobile, aimed to administer therapeutic table-top exercises to patients who have suffered injuries that affect the function of their upper extremities. The proposed mobile platform is a low-cost, portable, easy-to-use rehabilitation device targeted for home use. In particular, AssistOn-Mobile consists of a holonomic mobile platform with four actuated Mecanum wheels and a compliant, low-cost, multi-degrees-of-freedom series elastic element acting as its force sensing unit. Thanks to its series elastic actuation, AssistOn-Mobile is highly backdriveable and can provide assistance/resistance to patients, while performing omni-directional movements on plane. AssistOn-Mobile also features Passive Velocity Field Control (PVFC) to deliver human-in-the-loop contour tracking rehabilitation exercises. PVFC allows patients to complete the contour-tracking tasks at their preferred pace, while providing the proper amount of assistance as determined by the therapists. PVFC not only minimizes the contour error but also does so by rendering the closed-loop system passive with respect to externally applied forces; hence, ensures the coupled stability of the human-robot system. We evaluate the feasibility and effectiveness of AssistOn-Mobile with PVFC for rehabilitation and present experimental data collected during human subject experiments under three case studies. In particular, we utilize AssistOn-Mobile with PVFC (a) to administer contour following tasks where the pace of the tasks is left to the control of the patients, so that the patients can assume a natural and comfortable speed for the tasks, (b) to limit compensatory movements of the patients by integrating a RGB-D sensor to the system to continually monitor the movements of the patients and to modulate the task speeds to provide online feedback to the patients, and (c) to integrate a Brain–Computer Interface such that the brain activity of the patients is mapped to the robot speed along the contour following tasks, rendering an assist-as-needed protocol for the patients with severe disabilities. The feasibility studies indicate that AssistOn-Mobile holds promise in improving the accuracy and effectiveness of repetitive movement therapies, while also providing quantitative measures of patient progress.

In this paper I present a precise version of Stalnaker’s thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by ‘if A then B’ in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker–Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place.

I end the paper by suggesting that this approach overcomes some of the objections often levelled at accounts of indicatives based on the notion of similarity.

Recently, Chen, Hsiau & Yang [1] proposed a new two-urn model with red and white balls and showed that the fractions of red balls in both urns converge almost surely to the same limit. We extend the results for the two-urn model to the q-urn model (q≥3) with similar dynamics of drawing and adding balls. We use matrix forms and martingale theory to show that the fractions of red balls in all urns converge almost surely to the same limit.

We analyze optimal replacement and repair problems of semi-Markov missions that are composed of phases with random sequence and durations. The mission process is the minimal semi-Markov process associated with a Markov renewal process. The system is a complex one consisting of non-identical components whose failure properties depend on the mission process. We prove some monotonicity properties for the optimal replacement policy and analyze the optimal repair problem under different cost structures.

In this paper, we provide a new technique for analyzing the nonstationary Erlang loss queueing model with abandonment. Our method uniquely combines the use of the functional Kolmogorov forward equations with the well-known Gram-Charlier series expansion from the statistics literature. Using the Gram-Charlier series expansion, we show that we can estimate salient performance measures of the loss queue such as the mean, variance, skewness, kurtosis, and blocking probability. Lastly, we provide numerical examples to illustrate the effectiveness of our approximations.

In this paper, we study the instant availability A(t) of a repairable system by integral equation. We have proved initial monotonicity of availability, and derived lower bounds of A(t) and average availability. The availabilities of two systems are compared.

Single-support heel-off occurs when the heel of the trailing leg has been lifted from the ground around its toe, while the leading leg is still swinging forward. A similar gait event occurs during human walking, and is crucial to achieve a longer step length and a higher walking speed. In this paper, this crucial gait event is studied, specifically in how it influences the agility and the energy efficiency of bipedal walking. Toward this goal, the concept of limit-cycle bipedal walking which possesses natural and energy-efficient gaits is employed. The aforementioned concept is applied to a flat-foot bipedal model which is developed and actuated by a constant hip torque only during the single-support phase to walk on the ground. The impedance of each ankle is adjusted by using two springs, one at the back-side and the other at the front-side, as well as one damper. In comparison with point/round foot bipedal models, the flat-foot bipedal model produces more versatile limit-cycle gaits comprised of a number of gait series, each of which is a sequence detected among twelve gait postures dictated by the kinetics of the unilateral constraints at the heel, toe, or both. As a result of comprehensive simulations, it is concluded that single-support heel-off significantly improves the agility of bipedal walking because of the increase in the step length and the walking speed. Furthermore, even though limit-cycle gaits including single-support heel-off require higher energy input as compared with gaits excluding such an event, single-support heel-off significantly improves the energy efficiency of bipedal walking since the increase in the step length dominates the increase in the energy input.

This paper presents a new observer-based adaptive controller for handling an object with unknown geometry, center of mass, and inertia using a cooperative robotic system. The cooperative robotic system comprises three Cartesian robots, where robots and the grasped object form a closed-loop kinematic chain. The unknown object is approximated by three virtual links of unknown lengths rigidly attached to one another at the object's center of mass (COM). Due to the unknown COM and unknown inertia of the object, the lengths and inertia of these virtual links are unknown, resulting in kinematic and dynamic uncertainties in the control system. A parameter estimator is proposed to estimate the object's COM to compensate for kinematic uncertainties of the system. Moreover, a new dynamic adaptation law is developed to cope with dynamic uncertainties of the object. The dynamic equations of the cooperative system are transformed from joint space into task space. These task space dynamics are transformed into object space by passively decomposing the dynamics into two decoupled systems, i.e. locked and shaped systems. An adaptive controller is developed for the locked system, and the shaped system is controlled by a composite controller based on a PD controller plus a stabilizing damping term. The stability of the proposed controllers is shown using the passivity concept and Lyapunov theorem. Simulation results show that the closed-loop position error asymptotically converges to zero. It is also shown that kinematic and dynamic adaptation parameters converge to real and bounded values respectively.