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A reactionless machine will not apply reaction forces and moments on the mounting base during motion. This article presents the theory for design of a reactionless planar parallel mechanism. The salient features of this design are: (i) it uses auxiliary parallelograms to locate the center of mass of each leg at the base, (ii) choice of geometric and inertial parameters to satisfy the reactionless conditions and/or selection of trajectory to achieve a reactionless design. We illustrate the reactionless feature of such a mechanism through computer simulations.

In this paper, navigation and control of an autonomous mobile unicycle robot in an obstacle-ridden environment is considered. The unicycle dynamic model used has two differentially driven wheels, with the motor torques as the system input. Two novel potential-field-based controllers are derived, which stabilize the robot within a surrounding circular area (henceforth called a bubble) of arbitrary size. The first controller takes the unicycle to the center of its bubble, while the second corrects its orientation. The designed potentials also work with a kinematic model. Explicit bounds for permissible initial speeds are derived, such that maximum torque limits and/or maximum speed limits are not violated once the controller is activated. These controllers are then embedded in a navigation framework. An existing global planner is used to first create a string of variable-sized bubbles which connect the start point to the goal point, with each bubble's size indicative of the radial obstacle clearance available from its center. The robot then keeps itself within a fixed-sized bubble, which it then moves in discrete steps, according to the direction provided by the global plan, while repulsively avoiding unexpected obstacles. Hence, the gross movement is created by switching local potential-field-based controllers. This scheme is first verified in computer simulation of a single robot moving in a maze. It is then implemented on an experimental setup of robots equipped with proximity sensors. Results are presented to illustrate the effectiveness of the system.

This paper provides a framework for planning and control of formations of multiple unmanned ground vehicles with trailers to traverse between goal points in an idealized, disturbance-free environment. This framework allows on-line planning of the formations using the A* search algorithm based on current sensor data. The formation is allowed to dynamically change in order to avoid obstacles in the environment while minimizing a cost function aimed at obtaining collision-free and deadlock-free paths. Based on a feasible path for a leader of the group and the differential flatness property of a truck-tractor-trailer system, the trajectory planner satisfies the kinematic constraints of the individual vehicles while accounting for inter-vehicle collisions and path constraints. Also, optimization techniques are used to on-line change the path of the truck-tractor-trailer system. Illustrative simulations with simplified models of John Deere vehicles with trailers in formations are presented. Laboratory experiments are also performed on a 2-wheel differential drive mobile vehicle attached with a trailer cart on a flat, smooth floor using overhead cameras for precise references. The concluding section of the paper discusses some of the additional work needed to make the results applicable in a real-world environment.

A sit-to-stand assist device can serve the needs of people suffering from muscle weakness due to age or disabilities that make sit-to-stand a difficult functional task. The objective of this paper is to design a passive gravity-balancing assist device for sit-to-stand motion. In our study, it has been shown that the contribution to the joint torques by the gravitational torque is dominant during sit-to-stand motion. On the basis of this result, a gravity balanced assistive device is proposed. This passive device uses a hybrid method to identify the center-of-mass of the system using auxiliary parallelograms first. Next, appropriate springs are connected to the device to make the total potential energy of the system due to the gravity and the springs constant during standing up. A demonstration prototype with the underlying principles was fabricated to test the feasibility of the proposed design. The prototype showed gravity balancing and was tested by the authors. This prototype will be modified appropriately for clinical testing.

Biped robots are more versatile than conventional wheeled robots, but they tend to tip over easily. The dynamic stability of a biped robot needs to be maintained during walking. In this paper, a novel approach to compute dynamically stable walking motions of a planar six degree-of-freedom biped is presented. This approach is analytical and is based on the need for periodicity of the motion. The resulting gait satisfies the dynamic stability criteria. Sets of joint motions for different step sizes and speed of walking, i.e., quasi-statically and dynamically stable walking patterns, can be obtained.

Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots lot more challenging than their counter- part parallel actuated robots. In this brief, we look into the control design for a nonredundant cable-suspended robot under positive input constraints. The design is based on feedback linearization controllers augmented with a reference governor (RG). This RG operates in accordance with the receding horizon strategy, by generating admissible reference signals, that do not violate the input constraints. An important issue in implementing such an algorithm for nonlinear systems is to predict the system behavior in a computationally efficient way. We show that feedback lin- earization controllers with the RG can offer an efficient way to predict the system's future states, using the error dynamics of inner feedback loop. Finally, the effectiveness of the proposed method is illustrated by numerical simulation and laboratory experiments on a 6-degree-of-freedom cable suspended robot.

Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots more challenging than their counterpart parallel-actuated robots. In the case with redundant cables, feedback control laws can be designed to make all tensions positive while attaining desired control performance. This paper presents approaches to design positive tension controllers for cable suspended robots with redundant cables. Their effectiveness is demonstrated through simulations and experiments on a three degree-of-freedom cable suspended robots.

This work examines different screw systems and analyzes the possible subsets spanned by the various choices of a screw basis when the intensities of the wrenches, applied along the screws of the basis, are not allowed to change sign. Such sets arise in cable robotics, grasping and assembly. Convex screw spaces exhibit a surprising geometric variety, often even inside the same screw system.

This paper provides a practical framework for planning and control of formations of multiple unmanned ground vehicles to traverse between goal points in a dynamic environment. This framework allows on-line planning of the formation paths using search algorithm based on the current sensor data. The formation is allowed to dynamically change in order to avoid obstacles in the environment, while minimizing a cost function aimed at obtaining collision- and deadlock-free paths. Based on a feasible path for a leader of the group, the trajectory planner satisfies the kinematic constraints of the individual vehicles, while accounting for inter-vehicle collision and path constraints. Two algorithms are provided to generate smooth trajectories from discrete path sequences. A Lyapunov-based controller is designed to keep the vehicles on their planned trajectories. Illustrative simulations of groups of unmanned ground vehicles and their laboratory implementations with three unmanned ground vehicles are presented.

We present a systematic procedure for deriving the model of a cable transporter system with arbitrarily varying cable lengths. The Hamilton principle is applied to derive the governing equations of motion. The derived governing equations are nonlinear partial differential equations. The results are verified using the Newton law. The assumed mode method is used to obtain an approximate numerical solution of the governing equations by transforming the infinite-dimensional partial differential equations into a finite-dimensional discretized system. We propose a Lyapunov controller, based directly on the governing partial differential equations, which can both dissipate the vibratory energy during the motion of the transporter and guarantee the attainment of the desired goal point. The validity of the proposed controller is verified by numerical simulation.

A mechanism is presented that can generate insect winglike motion. This motion includes both flapping out of the stroke plane in addition to twist of the wing. The mechanism has a single degree of freedom and employs a five-bar mechanism in addition to an auxiliary four-bar mechanism. The parameters in the mechanism were optimized to generate a prescribed motion of the wing taken from a hawk moth kinematic flight data. A scaled model of the mechanism was fabricated to verify practical feasibility of the design. In future, we will miniaturize this mechanism on our flying-bird prototypes.

For conventional designs of robots, manipulator motions result in forces and moments on the base. These forces and moments may cause undesirable translation and rotation of the base. The objective of this paper is to systematically analyze the fundamentals of reactionless robots. Based on this analysis, a design of one distinct class of spatial robot is proposed. The design is achieved through appropriate choices of geometric and inertial parameters. Due to the underlying conservation laws, the trajectory must satisfy additional constraints. We illustrate the reactionless feature of this robot through computer simulations. We are also fabricating reactionless robots to illustrate the underlying concepts.

This paper describes the underlying theory of gravity balanced spatial robotic manipulators through a hybrid strategy which uses springs in addition to identification of the center of mass using auxiliary parallelograms. A significant contribution of this paper is to show that springs with fixed ends are sufficient to gravity balance a spatial mechanism if the hybrid method of gravity balancing is used where the center of mass is identified first through auxiliary parallelograms. Also, the system remains gravity balanced even if the orientation of the base is changed, i.e., the direction of the gravity is changed with respect to the base. Although the method can be applied to n link spatial serial manipulators, we apply the method for gravity compensation of two and three degrees-of-freedom (DOF) spatial manipulators. A prototype with the underlying principles of this paper was fabricated at the University of Delaware.

In this paper we present a workspace analysis methodology that can be applied for optimal design of cable-suspended planar parallel robots. The significant difference between regular parallel robots and cable-suspended parallel robots is that the cables in cable-suspended robots can only carry tension forces. The workspace of a planar cable robot is characterized as the set of points where a reference point of moving platform can reach with tensions in all suspension cables. In the design of cable-suspended parallel robots, the suspension points of the cables, size and shape of the moving platform are the design variables. The workspace area and global condition index are used as the objective functions to optimize the design parameters. The global condition index is a measure of isotropicity of the manipulator. The design variables are determined for different numbers of cables using both objective functions at a specified orientation and also at different orientations of moving platform. Experimental results to measure the workspace area demonstrate the effectiveness of this method.

This paper presents the design of a passive two leg orthosis to gravity balance human legs for use by subjects with both leg impairment. This design combines the use of auxiliary parallelograms to locate the center of mass along with springs to achieve balancing of each leg. The gravity balancing for all motions of the leg and pelvis is achieved by assuming the center of mass of the pelvis to be located on the line joining the two hip joints. A method for deriving the effectiveness of the gravity balancing due to practical limitations is also outlined. We illustrate the gravity balancing feature of the orthosis and examine the assumptions through computer simulations.

Cable robots have potential usage for loading and unloading of cargo in shipping industries. A novel six-degrees-of-freedom two-stage cable robot has been proposed by NIST for skin-to-skin transfer of cargo. In this paper, we look at a planar version of this two-stage cable robot. The disturbance motion from the sea is considered while modeling the dynamics of robot. The problem of robust control of the end-effector in the presence of unknown disturbances, along with maintaining positive tensions in the cables, is tackled using redundancy of cables in the system. Simulation results show the effectiveness of the control strategy.

As high-rise buildings continue to grow, the design and control of elevators to transport passengers safely, quickly, and comfortably still remains a challenging problem. An important issue in ‘elevatoring’ is to transport passengers with minimal residual motion once the elevator has reached its destination floor. A simple and elegant solution of the residual motion control problem can be given using the theory of δ-flatness. First, we present modeling and residual motion control with non-negative inputs of a cable transporter system, consisting of a rigid body (the object) connected by two flexible ropes. Then, we present results for a special case of the general transporter problem, the residual motion control of elevator. A laboratory scale experimental demonstration of the residual motion control is also presented in this paper.

In this paper, we study the design and workspace of a 6–6 cable-suspended parallel robot. The workspace volume is characterized as the set of points where the centroid of the moving platform can reach with tensions in all suspension cables at a constant orientation. This paper attempts to tackle some aspects of optimal design of a 6DOF cable robot by addressing the variations of the workspace volume and the accuracy of the robot using different geometric configurations, different sizes and orientations of the moving platform. The global condition index is used as a performance index of a robot with respect to the force and velocity transmission over the whole workspace. The results are used for design analysis of the cable-robot for a specific motion of the moving platform.

The objective of this paper is to study the dynamic simulation of a tether as it is deployed or retrieved by a winch on a satellite orbiting around earth. In an effort to understand the problem incrementally, the following three models were developed: (a) Model 1: A tether with constant length moves on earth in the plane of constant gravity; (b) Model 2: A tether is deployed from a drum on earth in the plane of constant gravity, i.e., length of the cable changes during deployment; (c) Model 3: A tether is deployed from a drum on an orbiting satellite. These models have been chosen to bring different aspects as well as levels of difficulty in the analysis. For example, in Model 1, the length of cable is fixed and the gravity direction is constant during motion. The equations of motion for this model are derived using Newton’s laws and Hamilton’s principle to show the equivalence of the two methods. In Model 2, free length of the cable changes during deployment. The changing length of the cable introduces coupled nonlinearities into the motion. Model 3 includes the orbital effect on the motion of deployed cable. Each of these three dynamic models characterized by partial differential equations are first converted to a finite number of ordinary differential equations using Ritz’s procedure and are then numerically integrated using Matlab ODE solvers.

Gravity balancing is often used in industrial machines to decrease the required actuator efforts during motion. In the literature, a number of methods have been proposed for gravity balancing that include counterweights, springs, and auxiliary parallelograms that determine the center of mass. However, these concepts have not yet been seriously applied to rehabilitation machines. This paper presents the underlying theory and design of an orthosis for the human leg that can fully or partially balance the human leg over the range of its motion. This design combines the use of auxiliary parallelograms to determine the center of mass along with springs to achieve a full or partial gravity balanced orthosis design. A first prototype has been constructed to demonstrate the effectiveness of the idea. Future prototypes will have parameters that will be tuned to the geometry and inertia of a human subject and be tailored to an individual's needs.

Researchers around the world have focused on autonomous agriculture with systems encompassing greenhouse, orchard, field, and other applications. Research has shown the potential and ability of the technology to allow a vehicle or selection of vehicles to follow a specified task. In this study, one aspect of the problem, that of operating a tractor-cart combination in conjunction with a small-grain combine harvester, was investigated. The tractor-cart combination and combine harvester application was selected because of the high fatigue and long duration aspects of the problem. Differential flatness-based formation following was tested in software and robotic simulation. The software simulation was based on an actual field track from a combine yield monitor and demonstrated the potential of the system. The robotic simulation used two iRobot Magellan Pro robots in an indoor environment and demonstrated that the methodology could be implemented in real time.

This study presents the development of second spine, an upper body assistive device for human load carriage. The motivation comes from reducing musculoskeletal injuries caused by carrying a heavy load on the upper body. Our aim was to design a wearable upper body device that can prevent musculoskeletal injuries during human load carriage by providing a secondary load pathway—second spine—to transfer the loads from shoulders to pelvis while also allowing a good range of torso motion to the wearer. Static analysis of the backpack and the second spine was first performed to investigate the feasibility of our concept design. The development of second spine had two considerations: load distribution between shoulders and pelvis, and preserving the range of torso motion. The design was realized using load bearing columns between the shoulder support and hip belt, comprising multiple segments interconnected by cone-shaped joints. The performance of second spine was evaluated through experimental study, and its biomechanical effects on human loaded walking were also assessed. Based on the findings from second spine evaluation, we proposed the design of a motorized second spine which aims to compensate the inertia force of a backpack induced by human walking through active load modulation. This was achieved by real-time sensing of human motion and actuating the motors in a way that the backpack motion is kept nearly inertially fixed. Simulation study was carried out to determine the proper actuation of motors in response to the human walking kinematics. The performance of motorized second spine was evaluated through an instrumented test-bed using Instron machine. Results showed a good agreement with simulation. It was shown that the backpack motion can be made nearly stationary with respect to the ground which can further enhance the effectiveness of the device in assisting human load carriage.

Now-a-days robotic exoskeletons are often used to help in gait training of stroke patients. However, such robotic systems have so far yielded only mixed results in benefiting the clinical population. Therefore, there is a need to investigate how gait learning and de-learning get characterised in brain signals and thus determine neural substrate to focus attention on, possibly, through an appropriate brain-computer interface (BCI). To this end, this paper reports the analysis of EEG data acquired from six healthy individuals undergoing robot-assisted gait training of a new gait pattern. Time-domain partial Granger causality (PGC) method was applied to estimate directed neural connectivity among relevant brain regions. To validate the results, a power spectral density (PSD) analysis was also performed. Results showed a strong causal interaction between lateral motor cortical areas. A frontoparietal connection was found in all robot-assisted training sessions. Following training, a causal "top-down" cognitive control was evidenced, which may indicate plasticity in the connectivity in the respective brain regions.

This paper presents a wearable upper body suit designed to assist in human load carriage. The two functions of the suit are: (i) load distribution between the shoulders and the waist, and (ii) reduction of the dynamic load on the waist during walking. These are achieved through two cable driven modules — passive and active — within a custom fitted shirt integrated with motion/force sensors, actuators, and a real time controller. The load distribution between the shoulders and the waist is achieved through the load bearing columns connecting the shoulder pads and the waist belt whose load bearing capacity is modulated by a nominal cable tension in the passive module via a ratchet mechanism. The dynamic load is reduced in addition in the active module by modulating the cable tension via external actuator. Mathematical model of the system is presented and a state feedback controller is designed. Simulation study was performed to investigate the system response under different disturbance conditions as a result of vertical motion of the waist during human walking. Experiment evaluation of the suit was performed with a subject walking on a treadmill while carrying a backpack load. The results show that the developed suit can transfer the load from the shoulders to the waist as well as reduce the dynamic load induced during human walking. This can potentially reduce the energy expenditure and the risk of musculoskeletal injuries associated with human load carriage.Copyright © 2015 by ASME

Some engineering applications require structures to expand and contract in size, while retaining their exterior shape. The applications range from mundane daily life objects to more fancy art structures. In contrast to a multi degree-of-freedom structure, a single degree-of-freedom structure can be driven by a single actuator, reducing cost and simplifying the control. In this paper, we study single degree-of-freedom structures that can be formed by a lattice of single degree-of-freedom polyhedral expanding units. Due to built-in symmetries, the entire structure can expand and contract as one of the units in the structure is actuated. The paper describes the design of polyhedral single degree-of-freedom systems, the structures of their dynamics/optimal control, and results from construction prototypes.

In recent years, using tools from linear and nonlinear systems theory, it has been shown that classes of dynamic systems in first-order forms can be alternatively written in higher-order forms, i.e., as sets of higher-order differential equations. Input-state linearization is one of the most popular tools to achieve such a representation. The equations of motion of mechanical systems naturally have a second-order form, arising from the application of Newton’s laws. In the last five years, effective computational tools have been developed by the authors to compute optimal trajectories of such systems, while exploiting the inherent structure of the dynamic equations. In this paper, we address the question of computing the neighboring optimal for systems in higher-order forms. It must be pointed out that the classical solution of the neighboring optimal problem is well known only for systems in the first-order form. The main contributions of this paper are: (i) derivation of the optimal feedback law for higher-order linear quadratic terminal controller using extended Hamilton-Jacobi equations; (ii) application of the feedback law to compute the neighboring optimal solution.

Serial multi-body systems can be driven by cables routed through the links to achieve the desired range of motion. Placement and routing of the cables alter the performance characteristics of the manipulator. There are possible applications for such mechanisms where low moving inertia is required. One of the challenges in the design of cable-driven mechanisms is to keep cables in tension during the motion. In this article, the addition of springs and its impact on workspace is investigated. A 2-link cable-driven robot is used to illustrate changes in Wrench Feasible Workspace (WFW) as springs are added between the serial manipulator and the ground or between the links.

The operational workspace of a cable-driven serial robot is largely dictated by the choice of cable placement and routing. As robot complexity increases with additional cables and degrees of freedom, the problem of designing a cable architecture can quickly become challenging. This paper builds upon a previously described methodology to identify and analyze optimal cable configurations, expanding the approach to a 3-DoF robot leg driven by four cables. The methodology is used to analyze configuration trends in the routing and placement of the cables which achieve the desired range of motion for the robot. The results of the analysis are used to inform the design of a cable architecture which is shown to be capable of controlling the robot through the desired task.

This study focuses on how the inertia force of a backpack induced by human walking can be compensated by active load modulation through a Second Spine, a device that provides an alternate pathway to transfer loads from the shoulder to the pelvis. Human walking induces periodic vertical acceleration of the upper body. A backpack worn on the upper body undergoes this same acceleration. Inertia force is induced by this acceleration and the human body has to sustain this motion and provide necessary energy. Based on this knowledge and our previous studies on a passive Second Spine, we present studies on a motorized Second Spine that can actively modulate the vertical motion of a backpack such that the inertia forces can be reduced. This is realized by real-time sensing and actuation so that the backpack is kept inertially fixed. The performance of such a device was evaluated on an instrumented test-bed using an Instron machine, showing results in good agreement with simulation. It was shown that the backpack motion can be made nearly stationary with respect to the ground by active modulation using motors and the inertia force is reduced.

This paper introduces the design of SoleSound, a wearable system designed to deliver ecological, audio-tactile, underfoot feedback. The device, which primarily targets clinical applications, uses an audio-tactile footstep synthesis engine informed by the readings of pressure and inertial sensors embedded in the footwear to integrate enhanced feedback modalities into the authors' previously developed instrumented footwear. The synthesis models currently implemented in the SoleSound simulate different ground surface interactions. Unlike similar devices, the system presented here is fully portable, and can therefore be utilized outside the laboratory setting. A first experimental evaluation indicates that the device can effectively modulate the perception of the ground surface during walking, thereby, inducing changes in the gait of healthy subjects.

Along with the coming of the aging society, the passive robot walking helper is introduced for providing safe mobility for the elderly, which features continuous energy dissipation from the system with brakes for steering. When this passive walking helper is applied for guidance and obstacle avoidance, it is crucial to determine proper braking torques in accordance with user-applied force for avoiding the obstacles and reaching the desired location. Motivated by it, in this paper, we propose such an approach based on receding horizon control. The proposed approach is efficient in braking torque derivation and allows the walking helper to stop at the goal with parking control. With the desired location to reach, the proposed scheme first plans a smooth path for the walking helper to follow based on Dubins curve [13]. The process of torque derivation is then formulated into solving an optimization problem with constraints that guarantee system passivity. When the walking helper detects the obstacles, the obstacle avoiding strategy is activated to bring it to deviate from them, which is achieved by including the constraints for obstacle avoidance into the optimization process. Simulations and experiments are performed to demonstrate the effectiveness of the proposed approach.

Self-initiated mobility is a causal factor in children’s development. Previous studies have demonstrated the effectiveness of our training methods in learning directional driving and navigation. The ultimate goal of mobility training is to enable children to be social, that is, to interact with their peers. A powered mobility device was developed that can localize itself, map the environment, plan an obstacle-free path to a goal, and ensure safety of a human driver. Combined with a positioning system, this system is able to apply a force field using a modular haptic feedback approach to train subjects to drive towards an object, a caregiver, a peer, or a group of peers. System feasibility was tested by designing a ‘ball chasing’ game. Results show that the system is promising in promoting socialization in children.

Due to lack of mobility, children are limited in their interaction with others. This lack of interaction with peers leads to emotional problems in children with special needs, behavior disorders, and social maladjustment. These social problems continue even when these children become adults. Hence, it is important to promote social skills at a very early age. In this study, we suggest a new training paradigm for young infants and toddlers seated on mobile robots, using force feedback joystick, to bring them closer to their peers so that it can facilitate interaction. Four healthy children participated in a game as they chase a caregiver. A haptic force feedback strategy teaches how to follow the caregiver. The force feedback guidance strategy is tested as a training tool to bring the children in close proximity to their peers.

An active Tethered Pelvic Assist Device (A-TPAD) has been presented in this paper. TPAD is a cable robot for studying force adaptation in human walking by applying external forces and moments on the human pelvis. A two stage control strategy was implemented to apply the desired force-moment profile. The controller includes (i) a quadratic programming based optimization scheme, (ii) a real-time human motion monitoring system and (iii) a PID feedback loop to plan and implement the required cable tensions. The control strategy was validated first by testing it on a dummy pelvis setup. A pilot experiment was then conducted with a human walking on a treadmill with A-TPAD. The goal was to apply a vertical downward force vector equivalent to 10% of subject’s body weight (BW ) at the pelvis. Results showed that the applied vertical force was acting downwards over the full gait cycle and was between 8-13% of the BW . Other force-moment components were maintained within a specified range during the experiment. Increased foot pressure was reported in the presence of vertical force. In summary, A-TPAD provides the capability of applying and controlling a desired force-moment profile on the human pelvis over a gait cycle.

Walking mechanics has been studied for a long time, being essentially simple but nevertheless including quite tricky aspects. During walking, muscular forces are needed to\ud support body weight and accelerate the body, thereby requiring a metabolic demand. In this paper, a new Constant Pushing Force Device (CPFD) is presented. Based on a novel actuation concept, the device is totally passive and is used to apply a constant force to the pelvis of a subject walking on a treadmill. The device is a serial manipulator featuring springs that provide gravity balancing to the device and exert a constant force regardless of the pelvis motion during walking. This is obtained using only two extension springs and no auxiliary links, unlike existing designs. A first experiment was carried out on a healthy subject to experimentally validate the device\ud and assess the effect of the external force on gait kinematics and timing. Results show that the device was capable of exerting an approximately constant pushing force, whose action affected subject’s cadence and the motion of the hip and ankle joints.

A trajectory optimization scheme based on the property of differential flatness is proposed in this paper. A dynamic optimization problem is transformed into a lower dimensional nonlinear programming problem through the use of flat outputs. This optimization approach is demonstrated in the repeated optimization of nonlinear dynamic systems under feedback in an approach similar to nonlinear model predictive control. This approach is illustrated on two examples involving biomass optimization and product optimization. Optimization under feedback is studied for the nominal problem and the case where uncertainty is present. The proposed scheme is also used in conjunction with a nonlinear Luenberger observer to generate the optimal trajectories under parametric uncertainty.

Using tools from systems theory, it is now well known that classes of linear and nonlinear dynamic systems in firstorder form can be alternatively written in higher-order form, i.e., as sets of higher-order differential equations. Input-state linearization is one of the popular tools to achieve such a transformation. For mechanical systems, the equations of motion naturally have a second-order form. For real-time planning and control, a higher-order form offers a number of advantages compared to the first-order form. In this paper, we address the question of trajectory optimization of higher-order systems with general nonlinear constraints. First, we develop the optimality conditions directly using their higher-order form. These conditions are then used to develop computational approaches. A general purpose program has been developed to benchmark computations between problems posed in alternate higher-order and firstorder forms. The program implements both direct and indirect methods and uses collocation in conjunction with a nonlinear programming solver. infancy. However, a few studies in the literature address this issue applied to limited classes of problems. For example, a direct method was used for PVTOL systems to compute the optimal solution, where the inequality constraints were not considered [3]. In recent work, Agrawal and coworkers have used the indirect method to compute the optimal solution in the absence of inequality constraints. In these studies, the system equations were explicitly embedded into the cost functional. The results from higher-order variational theory were used to find the optimality conditions [4]. This approach was applied successfully to linear systems ([5], [6]) and feedback linearizable nonlinear systems [7]. The purpose of this paper is to extend the optimality theory applicable to higher-order systems, without converting the system equations to the first-order form. Using the resulting optimality conditions, direct and indirect computational algorithms are developed and implemented. The same direct or indirect algorithm is used to solve the firstorder and the higher-order optimization problems, thereby, allowing to benchmark the computation requirements in a systematic manner.

This paper describes an experimental test-bed that was developed to assist and assess rehabilitation during physical and occupational therapy. A PUMA 260 robot was used with a controller and interface software developed in-house. The robot is designed to operate in two modes: (1) passive and (2) active. In the passive mode, the robot moves the subject's arm through specified paths. In the active mode, a subject guides the robot along a predefined path overcoming specified joint stiffness. In this mode, the controller compensates for gravity so that the robot can support its own weight in an arbitrary configuration. The developed graphical interface enables display of the current configuration of the robot in real-time, and allows us to customize experiments for a subject, and collect force and position data during an experiment. The results of a preliminary study with healthy subjects using this test-bed are also presented along with issues involved in the choice of paths and interpretation of the results.

A trajectory optimization scheme based on the property of differential flatness is proposed in this paper. A dynamic optimization problem is transformed into a lower dimensional nonlinear programming problem through the use of flat outputs. The optimization scheme is demonstrated on the optimization of biomass and product in fed-batch bioreactors. The proposed scheme is also used in conjunction with a nonlinear Luenberger observer to generate the optimal trajectories under parametric uncertainty.

It is shown in this paper that the finite-time optimal control of polynomial systems can be obtained by solving a sequence of optimal control problems for the linearized problem. The paper provides proof of convergence as well as illustration of the procedure by two examples.

This paper derives some optimization results for bilinear systems using a higher-order method by characterizing them over matrix Lie groups. In the derivation of the results, first a bilinear system is transformed to a left-invariant system on matrix Lie groups. Then, the product of exponential representation is used to express this system in canonical form. Next, the conditions for optimality are obtained by the principles of variational calculus. It is demonstrated that closed-form analytical solutions exist for classes of bilinear systems whose Lie algebra are nilpotent.

This paper presents a method for designing tremor suppression systems that achieve a specified reduction in pathological tremor power through controlling the impedance of the human-machine interface. Position, rate, and acceleration feedback are examined and two techniques for the selection of feedback coefficients are discussed. Both techniques seek a desired closed-loop human-machine frequency response and require the development of open-loop human-machine models through system identification. The design techniques were used to develop a tremor suppression system that was subsequently evaluated using human subjects. It is concluded that nonadaptive tremor suppression systems that utilize impedance control to achieve a specified reduction in tremor power can be successfully designed when accurate open-loop human-machine models are available.

Describes a prototype and analytical studies of a spherical rolling robot, a new design of a nonholonomic robot system. The spherical robot is driven by two remotely controlled, internally mounted rotors that induce the ball to roll and spin on a flat surface. It is tracked on the plane by an overhead camera. A mathematical model of the robot's motion was developed using the nonholonomic constraints on its motion. For a number of simple motions, it is shown experimentally that the model agrees well with the results. Methods were developed for planning feasible, minimum time and minimum energy trajectories for the robot. These methods are illustrated both by mathematical simulation and hardware experiments.

Congenital depression of the fetal skull unassociated with trauma is a rare event. In general, larger and deeper depressions are treated more aggressively either by neurosurgical correction or suction elevation with a breast pump. A case of right parietal skull depression noticed at birth in a term neonate born through cesarean section is reported here. Computed tomography scan revealed a bony depression without a fracture. The baby was managed conservatively, and the depression resolved completely at 6 months of age. This case highlights the potential role of spontaneous resolution in simple congenital skull depression.

This paper describes the design of an active gravity balanced planar mechanism, where auxiliary parallelograms are used to physically locate the center of mass of the mechanism. A sliding carriage positions a counterweight directly above the center of mass of the mechanism in order to make the system gravity balanced. The sliding carriage uses joint encoder data from the mechanism to compute the location of the center of mass. Experiment results demonstrate the effectiveness of the approach.