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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]

Impedance Control (IC) and Admittance control (AC) are two control methods for robot-environment interaction which have opposing performance and stability characteristics. Previous research has proposed that the two controllers define a spectrum of controllers. This paper quantifies the IC/AC spectrum as a trade-off between the suppression of force sensor error and modelling error. Unified Interaction Control (UIC) is introduced, which can interpolate across this spectrum of controllers by using a periodic state-reset and an inner-loop gain weighting parameter. The UIC is verified through simulation, experiment, and an eigenvalue analysis. Interpolating across the spectrum allows one to choose an ideal controller given the nature of the robot and environment. This is demonstrated in two case studies: adapting the level of interpolation to optimize performance with a changing environment, and using a static level of interpolation to mitigate the worst-case effects in both IC and AC. [ABSTRACT FROM AUTHOR]

The rapid growth in research exploiting deep learning to predict mechanical systems has revealed a new route for system identification; however, the analytic model as a white box has not been replaced in applications because of its open physical information. In contrast, the models generated by end-to-end learning usually lack the ability of physical analysis, which makes them inapplicable in many situations. Consequently, high-accuracy modeling with physical analyzability becomes a necessity. In this paper, we introduce bidirectional dynamic neural networks, a deep learning framework that can infer the dynamics of physical systems from control signals and observed state trajectories. Based on forward dynamics, we train the neural ordinary differential equations in a trajectory backtracking algorithm. With the trained model, the inverse dynamics can be calculated and based on Lagrangian Mechanics , the physical parameters of the mechanical system can be estimated, including inertia, Coriolis and centrifugal forces, and gravity. As a result, the model can seamlessly incorporate prior knowledge, learn unknown dynamics without human intervention, and provide information as transparent as analytic models. We demonstrate our method on simulated 2-axis and 6-axis robots to evaluate model accuracy, including physical parameters and verified its applicability on real 7-axis robots. The experimental results show that this method is superior to the existing methods. This framework provides a new idea for system identification by providing interpretable, physically consistent models for physical systems. [ABSTRACT FROM AUTHOR]

Legged manipulators are a prime candidate for reducing risk to human lives through completing tasks in hazardous environments. However, controlling these systems in real-world applications requires a highly functional teleoperation framework, capable of leveraging all utility of the robot to complete tasks. In this work, such a teleoperation framework is presented, where a wearable whole-body motion capture suit is integrated with a whole-body controller specialised for teleoperation and a set of teleoperation strategies that enable the control of all main frames of the robot along with additional functions. Within the whole-body controller, all tasks and constraints can be configured dynamically due to their modularity, hence enabling seamless transitions between each teleoperation strategy. As a result, this not only enables the realisation of trajectories outside the workspace without the whole-body controller but also the ability to complete tasks that would require an additional manipulator if just the gripper frames of the robot were controllable. To validate the presented framework, a set of real robot experiments have been completed to demonstrate all teleoperation strategies and analyse their proficiency. [ABSTRACT FROM AUTHOR]

We present a first-order recursive approach to sensitivity analysis based on the application of the direct differentiation method to the inverse Lagrangian dynamics of rigid multibody systems. Our method is simple and efficient and is characterized by the following features. Firstly, it describes the kinematics of multibody systems using branch connectivity graphs and joint-branch connectivity matrices. For most mechanical systems with an open-tree kinematic structure, this method turns out to be more efficient compared to other kinematic descriptions employing joint or link connectivity graphs. Secondly, a recursive sensitivity analysis is presented for a dynamic system with an open-tree kinematic structure and inverse dynamic equations described in terms of the Lagrangian formalism. Thirdly, known approaches to recursive inverse dynamic and sensitivity analyses are modified to include dynamic systems with external forces and torques acting simultaneously at all joints. Finally, the proposed method for sensitivity analysis is easy to implement and computationally efficient. It can be utilized to evaluate the derivatives of the dynamic equations of multibody systems in gradient-based optimization algorithms. It also allows less experienced users to perform sensitivity analyses using the power of high-level programming languages such as MATLAB. To illustrate the method, simulation results for a human body model are discussed. The shortcomings of the method and possible directions for future work are outlined. [ABSTRACT FROM AUTHOR]

A simple two-body model of a limbless crawler moving on an inclined rough plane is considered. The bodies are regarded as point masses. The system is controlled by the force of interaction of the bodies. Coulomb's friction force acts between the underlying plane and each of the bodies. The controllability of the crawler is investigated. It is proved that if no constraints are imposed on the control force, then the system can be driven from any initial state of rest on the plane into an arbitrarily small neighborhood of any prescribed terminal state of rest, provided that at the initial time instant the bodies do not lie on the common line of maximum slope. A control strategy that alternates infinitely slow (quasistatic) and infinitely fast motions is defined. It is important that the plane is inclined; on the horizontal plane, the two-body crawler is uncontrollable. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to generate desired periodic motions for torque-driven fully actuated mechanical systems. The proposed scheme is based on a recent control design method which relies on energy shaping plus damping injection. The energy regulation is formulated as a control objective and then the controller is designed. A change of coordinates and a suitable nonlinear damping injection design play a key role in generating the desired periodic motion. An interesting characteristic of the proposed scheme is that the periodic motion with a time-varying offset (trend component) can be specified by the user. This can be useful for mechanical systems that demand non-static periodic motion, for tasks such as obstacle avoidance or fluid mixing. Through the proposed methodology, the closed-loop system is expressed as a nonlinear autonomous differential equation and its stability is analyzed by using LaSalle's Theorem and the Poincaré-Bendixson criterion. Numerical simulations on a two-degree-of-freedom manipulator arm illustrate the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

Most holonomic Unmanned Aerial Vehicles (HUAVs) (usually small-scale), employ at least four high-power thrusting actuators, resulting in increased mass, inertia, and energy consumption. In this work, a novel design for a HUAV using only three high-power thrusting actuators is developed. The pointing dynamics of the high rpm motor-propeller assemblies are included in the analysis, resulting in the exposure of oscillatory gyroscopic dynamics. These are studied analytically to yield vectoring oscillation frequency estimates, useful in selecting actuators. A geometric, singularity free, control framework comprised of a new control-allocation scheme and a new vectoring controller is developed. Stability proofs are included and controller robustness is addressed. Simulations (MATLAB/GAZEBO) demonstrating the effectiveness of the developed design and control framework are provided; a HUAV with independent position/attitude regulation (full pose control) using only three thrusting actuators is showcased. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) have been attracting much attention and changing our daily lives. Recent technological advances in the development of UAVs have drastically increased both their general capabilities and areas of application. Among many others, one of the areas that benefits immediately from using UAVs could be remote inspection, since they can provide an alternative means of access to structures and collect data from locations difficult to reach for human inspectors. Lately, wall-climbing UAVs outfitted with contact-type sensors have been proposed to collect data for the periodic inspection and maintenance of buildings. However, the major drawback is that they can be used only for flat surfaces. In this paper, we present a lightweight robotic landing gear for enabling UAVs to land on irregular surfaces, without affecting the on-board flight control system that keeps the UAV in level flight during the entire mission. Our novel design uses a vacuum system for robotic landing gear to attach to the surface, and the movable counterweight composed of a vacuum motor and other control components to balance the flight. To lighten the total weight of UAV, the proposed robotic landing gear system has only one servo motor for gear operation and a passive mechanical structure that guides the vacuum suction cup at the frontal robotic legs to adapt to different shapes of surfaces. We present details of a prototype mechanism and landing experimental results under different scenarios generated within our laboratory environment. [ABSTRACT FROM AUTHOR]

The new applications of Clifford's geometric algebra surveyed in this paper include kinematics and robotics, computer graphics and animation, neural networks and pattern recognition, signal and image processing, applications of versors and orthogonal transformations, spinors and matrices, applied geometric calculus, physics, geometric algebra software and implementations, applications to discrete mathematics and topology, geometry and geographic information systems, encryption, and the representation of higher order curves and surfaces. [ABSTRACT FROM AUTHOR]

Sliding mode control is a very effective strategy in dealing not only with parametric uncertainties, but also with unmodeled dynamics, and therefore has been widely applied to robotic agents. However, the adoption of a thin boundary layer neighboring the switching surface to smooth out the control law and to eliminate the undesired chattering effect usually impairs the controller's performance and leads to a residual tracking error. As a matter of fact, underwater robots are very sensitive to this issue due to their highly uncertain plants and unstructured operating environments. In this work, Gaussian process regression is combined with sliding mode control for the dynamic positioning of underwater robotic vehicles. The Gaussian process regressor is embedded within the boundary layer in order to enhance the tracking performance, by predicting unknown hydrodynamic effects and compensating for them. The boundedness and convergence properties of the tracking error are analytically proven. Numerical results confirm the improved performance of the proposed control scheme when compared with the conventional sliding mode approach. [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]

The Generalized Voronoi Diagram (GVD) is a powerful environment representation, since, among other reasons, it defines a set of paths at maximal distance from the obstacles. Many works implicitly use this property to define safe navigation strategies for a mobile robot, but, in practice, only a few explicitly extract in real time the GVD from its perception to induce motion. This article addresses this challenge for a mobile robot solely equipped with an omnidirectional camera, and proposes an autonomous navigation strategy in unknown indoor and/or outdoor environments. The problem is formulated as a visual servoing task, and uses an anisotropic skeletonization algorithm to identify the projection in the image of the local GVD, while suppressing unsafe navigable paths thanks to a context-defined pruning parameter. Unlike rangefinder based system, the use of an omnidirectional camera allows to efficiently deal with outdoor scenes, since the navigable space is extracted using photometric cues. The servoing is then performed using a local linear approximation of the GVD, defined by a conic extracted in real time in the omnidirectional image. To assert the relevancy and efficiency of the proposed approach, extended experimental results are presented, both on indoor and outdoor scenarios. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal force and static friction are derived from the equations of motion for a rolling ball actuated by internal point masses that move inside the ball's frame of reference, and, as a special case, a rolling disk actuated by internal point masses. The masses may move along one-dimensional trajectories fixed in the ball's and disk's frame. The dynamics of a ball and disk actuated by masses moving along one-dimensional trajectories are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a global overview of mobile robot control and navigation methodologies developed over the last decades. Mobile robots have been a substantial contributor to the welfare of modern society over the years, including the industrial, service, medical, and socialization sectors. The paper starts with a list of books on autonomous mobile robots and an overview of survey papers that cover a wide range of decision, control and navigation areas. The organization of the material follows the structure of the author’s recent book on mobile robot control. Thus, the following aspects of wheeled mobile robots are considered: kinematic modeling, dynamic modeling, conventional control, affine model-based control, invariant manifold-based control, model reference adaptive control, sliding-mode control, fuzzy and neural control, vision-based control, path and motion planning, localization and mapping, and control and software architectures. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamics and motion planning for a spherical rolling robot with a pendulum actuated by two motors. First, kinematic and dynamic models for the rolling robot are introduced. In general, not all feasible kinematic trajectories of the rolling carrier are dynamically realizable. A notable exception is when the contact trajectories on the sphere and on the plane are geodesic lines. Based on this consideration, a motion planning strategy for complete reconfiguration of the rolling robot is proposed. The strategy consists of two trivial movements and a nontrivial maneuver that is based on tracing multiple spherical triangles. To compute the sizes and the number of triangles, a reachability diagram is constructed. To define the control torques realizing the rest-to-rest motion along the geodesic lines, a geometric phase-based approach has been employed and tested under simulation. Compared with the minimum effort optimal control, the proposed technique is less computationally expensive while providing similar system performance, and thus it is more suitable for real-time applications. [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]

Spring-loaded inverted pendulum (SLIP) template (and its various derivatives) could be considered as the mostly used and widely accepted models for describing legged locomotion. Despite their simple nature, as being a simple spring-mass model in dynamics perspective, the SLIP model and its derivatives are formulated as restricted three-body problem, whose non-integrability has been proved long before. Thus, researchers proceed with approximate analytical solutions or use partial feedback linearization when numerical integration is not preferred in their analysis. The key contributions of this paper can be divided into two parts. First, we propose a dissipative SLIP model, which we call as multi-actuated dissipative SLIP (MD-SLIP), with two extended actuators: one linear actuator attached serially to the leg spring and one rotary actuator attached to hip. The second contribution of this paper is a partial feedback linearization strategy by which we can cancel some nonlinear dynamics of the proposed model and obtain exact analytical solution for the equations of motion. This allows us to investigate stability characteristics of the hopping gait obtained from the MD-SLIP model. We illustrate the applicability of our solutions with open-loop and closed-loop hopping performances on rough terrain simulations. [ABSTRACT FROM AUTHOR]

An important issue in the field of motion control of wheeled mobile robots is that the design of most controllers is based only on the robot's kinematics. However, when high-speed movements and/or heavy load transportation are required, it becomes essential to consider the robot dynamics as well. The control signals generated by most dynamic controllers reported in the literature are torques or voltages for the robot motors, while commercial robots usually accept velocity commands. In this context, we present a velocity-based dynamic model for differential drive mobile robots that also includes the dynamics of the robot actuators. Such model has linear and angular velocities as inputs and has been included in Peter Corke's Robotics Toolbox for MATLAB, therefore it can be easily integrated into simulation systems that have been built for the unicycle kinematics. We demonstrate that the proposed dynamic model has useful mathematical properties. We also present an application of such model on the design of an adaptive dynamic controller and the stability analysis of the complete system, while applying the proposed model properties. Finally, we show some simulation and experimental results and discuss the advantages and limitations of the proposed model. [ABSTRACT FROM AUTHOR]

This paper is devoted to an experimental investigation of the motion of a rigid body set in motion by rotating two unbalanced internal masses. The results of experiments confirming the possibility of motion by this method are presented. The dependence of the parameters of motion on the rotational velocity of internal masses is analyzed. The velocity field of the fluid around the moving body is examined. [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]

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamic constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of intermediate points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the intermediate points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost. [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]

Intelligent mobility, agile manipulability, and increased autonomy are key technologies to guarantee for long-range and efficient surface exploration on Earth's Moon and on planets. In order to increase the scientific output of a rover mission it is very necessary to explore much larger surface areas reliably in much less time. This is the main driver for a robotics institute to combine mechatronics functionalities to develop an intelligent mobile vehicle with an appropriate number of wheels, and having specific kinematics and locomotion suspension depending on the operational terrain of the rover to operate. Moreover, a shift from a traditional bogie and wheel design to more agile wheel-legged combined systems seems to be beneficial to reach the goals. DLR's Robotics and Mechatronics Center has a long tradition in developing advanced components in the field of light-weight motion actuation, intelligent and soft manipulation and skilled hands and tools, perception and cognition, and in increasing the autonomy of any kind of mechatronic systems. The whole design is supported and is based upon detailed modelling, optimization, and simulation tasks. We have developed efficient software tools to simulate the rover driveability performance on various terrain characteristics such as soft sandy and hard rocky terrains as well as on slopes, where wheel and grouser geometry plays a dominant role. Moreover, first rover designs by best engineering intuitions has to be supported by means of optimization tools from the very beginning. By this, we optimize structural, geometric, and inertia parameters and we compare various kinematics suspension concepts, while making use of realistic cost functions like mass and consumed energy minimization, static stability, and more. For self-localization and safe navigation through unknown terrain we make use of fast 3D stereo algorithms that were successfully used in terrestrial mobile systems. The advanced rover design approach is applicable for lunar as well as Martian surface exploration purposes. [ABSTRACT FROM AUTHOR]

This paper aims at attaining one-leader & two-followers (1L-2F) formation control of multi-nonholonomic mobile robot (multi-NMR) systems subject to uncertainties and, at the same time, achieves trajectory-tracking of the leader NMR. To begin, the tracking error between the leader and a virtual reference robot is defined. Then, the extension to a leader-follower formation control structure is utilized to define the formation error (i.e., separation and orientation errors) between the leader and the followers. It has been proven that fuzzy sliding-mode tracking control (FSMTC) and backstepping formation control (BFC) can improve performance and stability when the overall closed-loop system is subject to uncertainties. Therefore, FSMTC and BFC are used for trajectory tracking of the leader NMR and formation control for two followers with respect to the leader, respectively. The stability of the closed-loop multi-NMR systems, i.e., trajectory tracking and formation control, is demonstrated through Lyapunov stability criteria. Finally, to validate the theoretical developments, computer simulations are conducted which prove the effectiveness, efficiency and robustness of the proposed scheme. [ABSTRACT FROM AUTHOR]

We consider the motion of a system consisting of a rigid body and internal movable masses on a rough surface. The possibility of rotation of the system around its center of mass due to the motion of internal movable masses is investigated. To describe the friction between the body and the reference surface, a local Amontons-Coulomb law is selected. To determine the normal stress distribution in the contact area between the body and the surface, a linear dynamically consistent model is used. As examples we consider two configurations of internal masses: a hard horizontal disk and two material points, which move parallel to the longitudinal axis of the body symmetry in the opposite way. Motions of the system are analyzed for selected configurations. [ABSTRACT FROM AUTHOR]

One factor that contributes to successful long-term human-human interaction is that humans are able to appropriately express their emotions depending on situations. Unlike humans, robots often lack diversity in facial expressions and gestures and long-term human robot interaction (HRI) has consequently not been very successful thus far. In this paper, we propose a novel method to generate diverse and more realistic robot facial expressions to help long-term HRI. First, nine basic dynamics for robot facial expressions are determined based on the dynamics of human facial expressions and principles of animation in order to generate natural and diverse expression changes in a facial robot for identical emotions. In the second stage, facial actions are added to express more realistic expressions such as sniffling or wailing loudly corresponding to sadness, laughing aloud or smiling corresponding to happiness, etc. To evaluate the effectiveness of our approach, we compared the facial expressions of the developed robot with and without use of the proposed method. The results of the survey showed that the proposed method can help robots generate more realistic and diverse facial expressions. [ABSTRACT FROM AUTHOR]

A nonholonomic model of the dynamics of an omniwheel vehicle on a plane and a sphere is considered. A derivation of equations is presented and the dynamics of a free system are investigated. An explicit motion control algorithm for the omniwheel vehicle moving along an arbitrary trajectory is obtained. [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]