This paper investigates the performance of a reduced-order fractional dynamic model for representing a large platooning system, with a focus on the relationship between the order of a fractional model and control gains used in the platooning system. For the large platooning system we modeled, each vehicle in the system applies an identical proportional-derivative (PD) controller and only responds to the immediately preceding vehicle. We employ an optimization-based method to find the best-matched model parameters under different PD control gains. Specifically, to avoid artifacts from the optimization process, we apply a hybrid particle swarm and pattern search method to optimize the model parameters. For comparison, we use a second-order differential equation model as a benchmark against our fractional-order model. The results show an intuitive relationship between the model’s fractional order and the control gains. Specifically, increasing the proportional gain kp leads to a higher fractional order, and increasing the derivative gain kd results in a lower fractional order. Moreover, the fractional reduced-order model outperforms the integer reduced-order model when the optimal fractional order lies between 1 and 2, especially in the middle. These results have the potential to lead us to find a better reduced-order model for platooning systems and provide more insight into solving difficult control problems such as string stability.

This paper presents a feed forward artificial neural network that identifies the order of the dynamics of a unit step response. The main contribution of this paper is demonstrating that a system trained on only integer order (first and second order) systems can identify fractional order responses with a high degree of accuracy. The details of the design of structure of the neural network, the training method and the training sets, as well as statistics describing the accuracy of the fractional predictions are presented. Also using the neural network to identify fractional dynamics for a large scale networked system from the authors’ prior work is presented as further validation and a demonstration of the applicability of the results. This demonstrates the potential for practicing engineers to use similar machine learning tools trained on "standard" systems with the ability to distinguish when features such as fractional order dynamics are significant and warrant deeper consideration for the design or control of such a system.

This paper proposes a method to efficiently compute the voltage and current along a transmission line which can be “damaged”; that is its electrical properties can be unevenly distributed. The method approximates a transmission line by a self-similar circuit network and leverages our previous work regarding the frequency response for that class of networks. The main motivation arises from research for railway track circuit systems where transmission line models are often employed. Determining deviations from baseline properties of the railway circuit is important for health monitoring of the system and furthermore, changes in circuit properties due to a train occupying a segment of the track also is of great interest as a means to ensure safety. Thus, in addition to monitoring the integrity of the railway circuit, our approach also could provide a means for safe operation in that it can be used to detect segments of the rail system that are occupied by trains.

This paper presents a new method for trajectory planning and control of a 2R planar horizontal robotic arm with only the first joint actuated, which is known to be controllable but not asymptotically stabilizable with smooth feedback controllers. The main idea is to first determine an admissible trajectory that satisfies both the constraints of system dynamics and boundary value conditions, and then design a feedforward controller for the system. For complex and highly nonlinear systems, an optimization method is applied to determine the trajectory. Moreover, a time-scaling method can be used to control the magnitude of the inputs and also make it easier to find a solution in the optimization procedure. To further improve the robustness of the controller, a feedback controller is designed along the planned trajectory. Position to position control of the robot is simulated to demonstrate the effectiveness of the method.

Most current bipedal robots were modeled with an assumption that there is no slip between the stance foot and ground. This paper relaxes that assumption and undertakes a comprehensive study of a compass gait biped with foot slipping. It is found that slips are most likely to happen near impact for a broad range of gaits. Among these gaits, ones with a backward swing foot velocity relative to the ground just before touch down generally require less friction to maintain stable walking than ones with a forward relative foot velocity. Moreover, a larger percentage of gaits with the "swinging backward" foot can tolerate some slipping without falling than those with a swinging forward foot at touch down. Thus, a gait with the swing-backward foot just before touch down should be more robust in the sense of preventing slipping and falling. It is further shown that only one parameter in gait design determines the swing-backward feature, which can help design robust gaits. Models with varying physical parameters such as mass, leg length, and position of center of mass (CoM), are also studied to validate the generality of the results.

This work presents a simple procedure for designing fractional PDμcontrollers for a type of implicit operators, which have recently been studied to describe large-scale systems. The methodology developed proposes a geometrical approach that allows characterizing the parameter-space of the PDμcontroller into stable and unstable regions. Several numerical examples illustrate the effectiveness of the proposed results.

This paper presents an approach to show global controllability of a class of underactuated mechanical systems. This class of systems include gymnastic robots and the classic cart-pole system. For this class of systems, we can define a connection point, and design a damping controller u(t) with the Lyapunov method to drive all states to the connection point. Further by exploiting the time reversal symmetry of the system and spline interpolation, a controller u(-t) can be obtained to drive the system from the connection point to any other state. The system is thus shown completely controllable, i.e., there exists an admissible trajectory from any given state to any given final state. Swing-up control designs for a pendubot, cart-pole system and triple pendulum are given as illustrative examples.

This paper presents a study of the relationship between the magnitude of coupling between the actuated and unactuated degrees of freedom for an ankle-actuated biped robot and the robustness and cost of transport of the gait. It extends prior results that considered only the instantaneous coupling at individual poses to analyze the cumulative effects of coupling over entire trajectories. The coupling metric is general in that it can be computed directly from the Lagrangian of the system. By using a two-link biped model, a family of ankle-actuated candidate gaits defined by fourth-order Bézier polynomials is generated, and the feasibility of the gaits is verified in the sense that the unilateral constraint of ground reaction force is satisfied. The correlation between the coupling metric and the maximum magnitude of disturbance that can be rejected is significant. It indicates that robust gaits tend to have small coupling under zero disturbance so that the “reserve” coupling may be utilized to reject the disturbance. Moreover, gaits with smaller cost of transport under zero disturbances have smaller coupling and therefore should be more robust.

This research seeks greater efficiency for walking robots. Efficiency can be improved in two ways: better performance (i.e., less wasted motion) and reduced energy consumption. Fractional-order control is a pathway to both of these improvements because of the flexibility it offers in designing a control strategy. Compared to the existing proportional-derivative architecture, changing the order of the derivative - the number of derivatives taken - to real numbers other than 1 has yielded both types of improvement for a simulated walker. The evidence of better performance is the leg angles' improvement in maintaining a desired relationship with respect to one another. Depending on the controller chosen, the walker can also be made to achieve the original level of performance with reduced control signals and less torque delivered to the hip joint, implying greater energy efficiency.

The dynamics of many large-scale robotic formation systems, including structured systems as well as some random scale-free networks of agents, can be accurately described using fractional-order differential equations. A fractional-order differential equation can contain derivative terms with non-integer order, e.g., the one-half derivative. This paper demonstrates that the fractional order of the dynamics of a system may be a potentially powerful new way to monitor the operational status of such systems. When the order of the system changes, it can indicate an important change in the status of the system. Integer-order models will never exhibit a change in order because the order is dictated by a natural first principle and the structure of the system. For this reason, traditional health monitoring tools essentially focus on identifying parameter variations in a mathematical description of the system, but not changes in order. When fractional-order models are considered, the infinite number of possible real-valued orders between any two integer orders may capture essential changes in the system's dynamics. This paper provides an example of such changes, provides a theoretical justification for the approach, and explores possible limitations to the approach.

This paper computes all the continuous point-transformation symmetries for a planar multi-agent dynamical control system. The relative configuration among the agents is often the most important aspect of this problem, and this paper presents a method to “factor out” the location and orientation on the plane of a multi-agent formation problem. This is useful in the case where only the relative positioning of the agents is of concern. The method to compute the symmetries and determine the reduced coordinates is well-established. The contributions of this paper are (1) computing the symmetries for a multi-agent system, (2) highlighting the utility of the reduction for the formation control application such as formation stability and (3) analyzing the symmetries to determine a relatively broad class of systems which have the same symmetries and hence identical coordinates for reduction. Although it has been addressed in various ways, essentially all methods to determine the stability properties of the formation control problem need the dynamics to be formulated on a reduced, relative space. Hence, stability (and stability-like notions such as that which follow from LaSalle's Principle) analyses will be the main beneficiary of this work.

Differential equations with fractional-order derivatives, e.g., the "one-half" derivative, have a long history in mathematics, but have not yet attained mainstream use in engineering and applied science. While applications do exist in modeling specific phenomena such as visco-elasticity and other types of difficult-to-model phenomena, and extensions to control such as in fractional-order PID do exist, everyday use of fractional order modeling is uncommon. A subset of complex systems called Cyber-Physical Systems (CPS) is receiving much emphasis in the research community. In this paper we show examples of networked system models which exhibit fractional-order dynamic responses. This suggests that fractional-order dynamics may be prevalent in CPS and hence may be an important and useful modeling tool in that area. We particularly focus on a scale free networked system.

This paper shows that a fractional-order differential equation may be used to accurately model the dynamic relationship between the first and last generations in a fleet of coordinating robots, even when the individual robots and interconnections have the usual integer-order dynamics. Such a fractional-order model offers the possibility of general applicability, particularly in the case of heterogeneous fleets of robots. Such systems tend to be very high order, and therefore model reduction is useful in modeling, simulation and control. Results are presented for the system considered illustrating that the fractional-order model achieves significant computational savings compared to simulating the full system.

System integration is the elephant in the china store of large-scale cyber-physical system (CPS) design. It would be hard to find any other technology that is more undervalued scientifically and at the same time has bigger impact on the presence and future of engineered systems. The unique challenges in CPS integration emerge from the heterogeneity of components and interactions. This heterogeneity drives the need for modeling and analyzing cross-domain interactions among physical and computational/networking domains and demands deep understanding of the effects of heterogeneous abstraction layers in the design flow. To address the challenges of CPS integration, significant progress needs to be made toward a new science and technology foundation that is model based, precise, and predictable. This paper presents a theory of composition for heterogeneous systems focusing on stability. Specifically, the paper presents a passivity-based design approach that decouples stability from timing uncertainties caused by networking and computation. In addition, the paper describes cross-domain abstractions that provide effective solution for model-based fully automated software synthesis and high-fidelity performance analysis. The design objectives demonstrated using the techniques presented in the paper are group coordination for networked unmanned air vehicles (UAVs) and high-confidence embedded control software design for a quadrotor UAV. Open problems in the area are also discussed, including the extension of the theory of compositional design to guarantee properties beyond stability, such as safety and performance.

This paper extends some prior work by the authors to address general robustness of solutions in multiagent coordination control problems. In particular, it focuses on fault-tolerant formation control. In our prior work, symmetries in the system were exploited to simplify the nonlinear Lyapunov stability analysis for symmetric systems. The type of symmetry considered is a discrete symmetry where the system is composed of many repeated instances of interacting identical agents. The results are based on Lyapunov methods, and hence are of general applicability and specifically these results are applicable to both distributed as well as non-distributed coordination methods. This paper considers the same types of systems and extends the stability results to the cases of robustness of formation stability under failure of individual agents.

A mobile manipulator is at the present time a widespread term to refer to robot systems built from a robotic manipulator arm mounted on a mobile platform. A mobile manipulation system offers a dual advantage of mobility offered by a mobile platform and dexterity offered by the manipulator. In this work, the tracking and nonlinear disturbance decoupling problems are studied. We show that this system posses the necessary geometric structure for complete disturbance decoupling between the outputs and disturbances. Simulation results obtained for the mobile manipulator show good performance in the presence of significant disturbances using the designed nonlinear controller.

This paper presents the relatively rich and interesting bifurcation structure that is present in the nature of optimal solutions to a multi-robot formation control problem. The problem considered is a two point nonlinear boundary-value problem that can only be solved numerically. Since common numerical solution techniques such as the shooting method are local in nature and hence are difficult to use to find multiple solutions, an alternative formulation of the problem is presented that can be solved through homotopy methods for polynomial systems. These methods are guaranteed to find all solutions within the resolution of the system description's discretization. Specifically, this paper studies a group of unicycle-like autonomous mobile robots operating in a 2-dimensional obstacle-free environment. Each robot has a predefined initial state and final state and the problem is to find the optimal path between two states for every robot. The path is optimized with respect to the control effort and the deviation from a desired formation. The bifurcation parameter is the relative weight given to penalizing the deviation from the desired formation versus control effort. It is shown that as this number varies, bifurcations of solutions are obtained. Considering the common use of optimization methods in robotic navigation and coordination problems, understanding the existence and structure of bifurcating and multiple solutions is of great importance in robotics.

This paper presents the definition of a new type of dynamic singularity for robotic manipulators. It is applicable to all underactuated robotic systems that can be described by Lagrange's equations where the Lagrangian is the kinetic minus potential energy. The approach is to decompose the velocity at every point in the configuration space into velocity directions that can be directly controlled and those that are uncontrolled and orthogonal to the directly controlled directions. These uncontrolled directions are controlled only through the dynamic coupling with the controlled directions and the measure of a dynamic singularity is then a measure of this degree of coupling. When this coupling is zero, the mechanism is said to be at a dynamic singularity. The practical implication is that, at such points, the dynamics are decoupled and control over the uncontrolled directions is very weak in that the mechanism will have to move away from the singularity before the inputs can affect the uncontrolled velocity directions. An example that is realistically complicated is presented and simulations show the effect on control inputs when the system is operating near a dynamic singularity.

This paper presents initial results in the novel integration of nonholonomic and stratified motion planning, fuzzy control and tactile sensing to construct a robotic manipulation system that is designed to be both dexterous and robust. It is dexterous in that it is fully nonlinear, can explicitly incorporate discontinuities in the motion planning i.e., finger gaiting, and allows rolling finger contacts. The sensing and fuzzy controller are intended to provide robustness that is necessary for real-world manipulation tasks that are characterized by modeling errors and are subjected to unmodeled external disturbances. The method is demonstrated experimentally using a set of four robots with end-effectors equipped with force sensors to provide feedback to the fuzzy supervisory control system.

Metabolism modeling has the potential to provide guidance on medicine manufacture and medical treatment in an efficient and economic way. A pancreas model developed from a mathematical description of the relevant physiology will demonstrate insulin dynamics and provide a platform for comparing metabolic abilities among different health conditions. As a part of whole body metabolism model, the pancreas model is composed of three compartments: insulin clearance (Id), generation (Ig) and release into plasma (Ir). Based on data from intravenous glucose tolerance tests (IVGTT) available in the literature, a deterministic optimal search method called DIRECT (Dividing RECTangles) was implemented to find the model parameters. Validation was performed on data sets that are different from those used for the optimization.

We obtain an intrinsic vector-valued symmetric bilinear form that can be associate with an underactuated simple mechanical control system. We determine properties of the form which serve as necessary conditions for driving underactuated simple mechanical control systems to rest. We also determine properties of the form that serve as sufficient conditions for driving a simple mechanical systems underactuated by one control to an epsiv-neighborhood of rest from an arbitrary initial configuration and velocity. These conditions are computable and coordinate invariant. We focus on the case where the symmetric form is real-valued and indefinite on the entire configuration manifold. Our technical results give rise to a nonlinear control law that drives these systems to an epsiv-neighborhood of rest given an arbitrary initial configuration, velocity and epsiv > 0.

This paper presents an extension of stratified motion planning results to the case where the base manifold upon which the motion planning occurs is not smooth. Robotic applications of this work include motion planning for legged robots over known, nonsmooth terrain and manipulation of nonsmooth objects with multiple robotic manipulators.

This paper develops a motion planning algorithm which exploits symmetry in distributed systems to reduce complexity and motion planning design time. The motion planning computations are carried out on a reduced order system, then extended to larger-order equivalent systems in such a way that the objectives of the larger system are satisfied and collision avoidance is guaranteed. The algorithm maintains a rigid body formation as a group robots follows a specified trajectory at the beginning and end of the trajectory. At this point, our algorithm is open loop. A simulation of four robots maintaining a square formation is presented to demonstrate the utility of the algorithm.

This paper presents a novel robotic platform for experimental research in large-scale distributed robotics and mobile sensor networks. The MICAbot is both inexpensive and flexible making it useful for a wide range of experimental goals. In this paper, we provide a description of the MICAbot design. Furthermore, we also discuss general design considerations involved in designing large-scale distributed robots focusing on cost, size, and functionality.

This paper presents experimental demonstrations and verification of a vision-based stratified motion planning method for the case where the base manifold upon which the motion planning occurs is not smooth. Robotic applications of the method include motion planning for legged robotics over non-smooth (but known) terrain and manipulation of non-smooth objects with multiple robotic manipulators. Experimental results with multiple robots manipulating a common non-smooth object are presented.

This paper considers the "reduction" problem for distributed robotic systems. In particular, the controllability of systems containing multiple instances of identical robotic systems or components where the overall system is invariant with respect to interchanging these identical robots or components is considered. The main result is a proposition which shows that for an equivalence class of symmetric systems of this type, the controllability of the entire class of systems can be determined by analyzing the smallest member of the equivalence class.

Presents an extension of the authors' previous stratified motion planning results to the case where the base manifold upon which the motion planning occurs is not smooth. Robotic applications of this work includes motion planning for legged robots over non-smooth (but known) terrain and manipulation of non-smooth objects with multiple robotic manipulators.

This paper addresses a three-dimensional implementation that results in several separate manipulators, each with intermittent contact with a central object of known geometry, cooperatively manipulating the object to a desired new position and orientation. Rolling control of an object using redundant contact of several independent manipulators is made difficult by the hybrid nature of this system that introduces complexity to the trajectory-planning problem, and by imperfection in the kinematic models which are needed to achieve such trajectory planning. The former is a theoretical problem which has been solved using Lie-algebra-based strategies to plan motion for the stratified systems. Imperfection in the kinematic models, on the other hand, leads to a practical implementation problem since even small errors in the equations that relate the internal pose of the robot to the position of the end-effector make precise sustained contact with an object difficult. The consequent lack of control of contact force combined with frictional unpredictability associated with rolling, causes gradual growth in the disparity between actual and calculated position and orientation of the object. A robust means for applying vision to compensate for imperfections in the holonomic kinematics of the robots as well as to update estimates of the pose of the object is outlined. Experimental results are also presented.

We present a general motion planning algorithm for robotic systems with a "stratified" configuration space. Such systems include quasi-static legged robots and kinematic models of object manipulation by finger repositioning. Our method is an extension of a nonlinear motion planning algorithm for smooth systems to the stratified case, where the relevant dynamics are not smooth. The method does not depend upon the number of legs or fingers; furthermore, it is not based on foot placement or finger placement concepts. Examples demonstrate the method.

This paper presents the development and experimental verification of a general control framework for robotic grasping and manipulation problems where "fingers" manipulate a grasped object. The method is general in that it is independent of object and finger geometries. Application of the method in simulation and to a real experimental platform are presented.

The purpose of this paper is to develop methods to reduce the complexity of nonlinear distributed systems by using symmetry properties within the system. A method for contracting and expanding controllable nonlinear systems is developed which maintains the controllability of the original system. In fact, it is shown that an entire equivalence class of symmetric nonlinear distributed control systems can be determined by checking the controllability of only one of its members. A group of mobile robots is used to demonstrate the utility of methods presented.

We show how motion planning and control ideas for smooth nonholonomic systems can be extended to legged quasi-static locomotion via the notion of "stratified" configuration spaces and "stratified" control theory. We particularly consider "minimalist" legged systems, which are not well handled by conventional theories based on foot placement. We briefly discuss controllability issues, and then present a motion planning algorithm for stratified systems. The method does not depend upon the number of legs, nor is it based on foot placement concepts.

We present a general method for determining controllability of a class of kinematic legged robots. The method is general in that it is independent of the robot's morphology; in particular, it does not depend upon the number of legs. Our method is based on an extension of a nonlinear controllability test for smooth systems to the legged case, where the relevant mechanics are not smooth. Our extension is based on the realization that legged robot configuration spaces are stratified. The result is illustrated with a simple example.

We present a general trajectory generation scheme for a class of "kinematic" legged robots. The method does not depend upon the number of legs, nor is it based on foot placement concepts. Instead, our method is based on an extension of a nonlinear trajectory generation algorithm for smooth systems to the legged case, where the relevant mechanics are not smooth. Our extension is based on the realization that legged robot configuration spaces are stratified. The algorithm is illustrated with a simple example.