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In spite of its intrinsic complexities, the passive gait of bipedal robots on a sloping ramp is a subject of interest for numerous researchers. What distinguishes the present research from similar works is the consideration of flexibility in the constituent links of this type of robotic systems. This is not a far-fetched assumption because in the transient (impact) phase, due to the impulsive forces which are applied to the system, the likelihood of exciting the vibration modes increases considerably. Moreover, the human leg bones that are involved in walking are supported by viscoelastic muscles and ligaments. Therefore, for achieving more exact results, it is essential to model the robot links with viscoelastic properties. To this end, the Gibbs-Appell formulation and Newton's kinematic impact law are used to derive the most general form of the system's dynamic equations in the swing and transient phases of motion. The most important issue in the passive walking motion of bipedal robots is the determination of the initial robot configuration with which the system could accomplish a periodic and stable gait solely under the effect of gravitational force. The extremely unstable nature of the system studied in this paper and the vibrations caused by the impulsive forces induced by the impact of robot feet with the inclined surface are some of the very serious challenges encountered for achieving the above-mentioned goal. To overcome such challenges, an innovative method that uses a combination of the linearized equations of motion in the swing phase and the algebraic motion equations in the transition phase is presented in this paper to obtain an eigenvalue problem. By solving this problem, the suitable initial conditions that are necessary for the passive gait of this bipedal robot on a sloping surface are determined. The effects of the characteristic parameters of elastic links including the modulus of elasticity and the Kelvin-Voigt coefficient on the walking stability of this type of robotic systems are also studied. The findings of this parametric study reveal that the increase in the Kelvin-Voigt coefficient enhances the stability of the robotic system, while the increase in the modulus of elasticity has an opposite effect. [ABSTRACT FROM AUTHOR]

We give a geometric account of kinematic control of a spherical rolling robot controlled by two internal wheels just like the toy robot Sphero. Particularly, we introduce the notion of shape space and fibers to the system by exploiting its symmetry and the principal bundle structure of its configuration space; the shape space encodes the rotational angles of the wheels, whereas each fiber encodes the translational and rotational configurations of the robot for a particular shape. We show that the system is fiber controllable—meaning any translational and rotational configuration modulo shapes is reachable—as well as find exact expressions of the geometric phase or holonomy under some particular controls. We also solve an optimal control problem of the spherical robot, show that it is completely integrable, and find an explicit solution of the problem. [ABSTRACT FROM AUTHOR]

Instability and risk of fall during standing and walking are common challenges for biped robots. While existing criteria from state-space dynamical systems approach or ground reference points are useful in some applications, complete system models and constraints have not been taken into account for prediction and indication of fall for general legged robots. In this study, a general numerical framework that estimates the balanced and falling states of legged systems is introduced. The overall approach is based on the integration of joint-space and Cartesian-space dynamics of a legged system model. The full-body constrained joint-space dynamics includes the contact forces and moments term due to current foot (or feet) support and another term due to altered contact configuration. According to the refined notions of balanced, falling, and fallen, the system parameters, physical constraints, and initial/final/boundary conditions for balancing are incorporated into constrained nonlinear optimization problems to solve for the velocity extrema (representing the maximum perturbation allowed to maintain balance without changing contacts) in the Cartesian space at each center-of-mass (COM) position within its workspace. The iterative algorithm constructs the stability boundary as a COM state-space partition between balanced and falling states. Inclusion in the resulting six-dimensional manifold is a necessary condition for a state of the given system to be balanced under the given contact configuration, while exclusion is a sufficient condition for falling. The framework is used to analyze the balance stability of example systems with various degrees of complexities. The manifold for a 1-degree-of-freedom (DOF) legged system is consistent with the experimental and simulation results in the existing studies for specific controller designs. The results for a 2-DOF system demonstrate the dependency of the COM state-space partition upon joint-space configuration (elbow-up vs. elbow-down). For both 1- and 2-DOF systems, the results are validated in simulation environments. Finally, the manifold for a biped walking robot is constructed and illustrated against its single-support walking trajectories. The manifold identified by the proposed framework for any given legged system can be evaluated beforehand as a system property and serves as a map for either a specified state or a specific controller's performance. [ABSTRACT FROM AUTHOR]

A growing interest within the space community focuses on robotics due to the large number of possible applications in many mission scenarios. On-Orbit Servicing (OOS) is arguably the most appealing implementation of space automatic systems. In several cases, OOS requires the capture of orbital objects, which is a complex and risky operation that can be successfully performed by robotic manipulators. Soft robotics, in particular, seems to be suitable for such applications given its intrinsic compliance to the operative environment. Devices based on Dielectric Elastomers (DE) can be employed for the implementation of soft robotic systems and showed promising performances. The introduction of DEs to orbital systems would represent a breakthrough in space technologies. In addition, space conditions could further advantage DE robotics, given the reduced environmental loads experienced and the longer times for operations. Nevertheless, Dielectric Elastomer Actuators (DEA) are a low-TRL (Technology Readiness Level) technology that needs to prove its maturity and suitability to space implementation. In this work, the performances of a redundant manipulator based on DEAs are presented in terms of numerical and experimental results. A 4-DoF planar manipulator has been tested in a gravity-compensated setup. The system is composed by two double-cone actuators mounted in series, each of them providing actuation of two DoF. The end-effector is an optical marker whose position is detected by a vision system. The system has a total of four joint DoF and operates in the xy horizontal plane; only the x and y positions of the end-effector are controlled. Two degrees of redundancy are obtained and exploited for the optimization of joint torques to avoid the saturation of actuators. Numerical simulations have been conducted to predict the system behaviour. The laboratory facility emulates the zero-gravity orbital environment by means of a suspending cable. Detailed experimental results are presented and exploited for the validation of control algorithm and numerical models. [ABSTRACT FROM AUTHOR]

Slow and accurate finger and limb movements are essential to daily activities, but the underlying mechanics is relatively unexplored. Here, we develop a mathematical framework to examine slow movements of tendon-driven limbs that are produced by modulating the tendons' stiffness parameters. Slow limb movements are driftless in the sense that movement stops when actuations stop. We demonstrate, in the context of a planar tendon-driven system representing a finger, that the control of stiffness suffices to produce stable and accurate limb postures and quasi-static (slow) transitions among them. We prove, however, that stable postures are achievable only when tendons are pretensioned, i.e., they cannot become slack. Our results further indicate that a non-smoothness in slow movements arises because the precision with which individual stiffnesses need to be altered changes substantially throughout the limb's motion. [ABSTRACT FROM AUTHOR]

This paper presents a unified geometric framework to input-output linearization of open-chain multi-body systems with symmetry in their reduced phase space. This leads us to an output tracking controller for a class of underactuated open-chain multi-body systems with holonomic and nonholonomic constraints. We consider the systems with multi-degree-of-freedom joints and possibly with non-zero constant total momentum (in the holonomic case). The examples of these systems are free-base space manipulators and mobile manipulators. We first formalize the control problem, and rigorously state an output tracking problem for such systems. Then, we introduce a geometrical definition of the end-effector pose and velocity error. The main contribution of this paper is reported in Section 5, where we solve for the input-output linearization of the highly nonlinear problem of coupled manipulator and base dynamics subject to holonomic and nonholonomic constraints. This enables us to design a coordinate-independent controller, similar to a proportional-derivative with feed-forward, for concurrently controlling a free-base, multi-body system. Finally, by defining a Lyapunov function, we prove in Theorem 3 that the closed-loop system is exponentially stable. A detailed case study concludes this paper. [ABSTRACT FROM AUTHOR]

Protein Misfolding Cyclic Amplification is a procedure used to accelerate the prion-replication process involved during the incubation period of transmissible spongiform encephalopathies. This technique could be used to design an efficient diagnosis test detecting the abnormally-shaped protein responsible of the decease before the affected person is at an advanced stage of the illness. In this paper, we investigate the open problem to determine what is the optimal strategy to produce maximum replication in a fixed time. Primarily, we expand on prior attempt to answer this question in general, and provide results under some specific assumptions. [ABSTRACT FROM AUTHOR]

We discuss the dynamics and stability of a rigid rimless spoked wheel, or regular polygon, confined to 'rolling' in a vertical plane uphill or downhill. The wheel has smooth inverted pendulum motions punctuated by repeated dissipative spoke impacts. It is a simple mechanical analogue to legged locomotion. The problem is completely soluble in closed form. We derive a return map for the full nonlinear system. The map has two asymptotically stable fixed points whose existence depends on slope angle: (1) standing still on two spokes and (2) limit cycle motion. For small slopes, only standing still exists; for intermediate slopes, the fixed points coexist; and, for large slopes, only limit cycles exist. We also completely define their basins of attraction. The rimless wheel's dynamical behaviour is analogous to two other dissipative systems, one smooth (a constantly forced, damped pendulum) and the other non-smooth (a 2D discrete skate). [ABSTRACT FROM AUTHOR]