This paper describes a parallel-actuated robotic mechanism designed to provide two degrees-of-freedom (DOF) to the end-effector relative to a fixed base. In a potential application as a head-neck traction brace, these two independent DOFs are the vertical translation of the head with respect to shoulders and a specified orientation of the head in lateral bending. Motivated by recommended clinical methods to apply traction forces on the head, it is designed to provide vertical traction force on the head while tilted in a specific orientation. The design has four chains starting from a base stationed at the shoulders, each chain having 5 DOFs. Each chain imposes a single constraint on the motion of the end-effector. Together, four chains would apply four constraints, allowing only two DOFs of motion to the end-effector. Two out of four component chains are actively driven by linear actuators. Our kinematic studies show that the achievable workspace of this mechanism with a specific stroke length of actuators of ± 50 mm results in 175-222 mm of vertical translation and up to ± 9◦of lateral bending. The lateral bending is coupled to the flexion/extension angle of the end-effector. A physical prototype was constructed to investigate the functional realization of the design in hardware. Overall, the physical prototype validated the motion of the theoretical model despite potential errors in the fabrication, making the design a candidate for potential head-neck traction application.

Human performance and body motions when submerged underwater are highly influenced by buoyancy forces. In this article, we simulate the effect of buoyancy on human motion over ground by using a cable-driven robotic system. The robotic platform was configured to apply buoyancy forces on the human torso, similar to underwater, while subjects performed reaching and assembly tasks. Previous studies have analyzed muscle activity, postural balance, and limb kinematics in aquatic enclosures. However, from these studies, it is difficult to correlate observed human physiology changes with a specific underwater feature. The goal of this article is to expand our knowledge in objectively characterizing how physical underwater features affect human performance. The results of this article could help in designing more efficient overground programs to train divers in performing submarine motor tasks. For this purpose, we investigated motion of body center of mass (COM), ground reaction forces, muscular activity with surface electromyography (sEMG), and limb coordination while participants performed reaching tasks with and without simulated underwater forces. Within the simulated underwater environment with the cable system, buoyancy force significantly displaced the COM to outside the base of support. Additionally, ground reaction forces and sEMG of back muscles were significantly reduced during this condition. The results obtained in the present study are in line with previous experiments performed underwater. The results show the potential applicability of cable-driven platforms to expand our understanding in the future about the influence of aquatics on functional tasks.

Wearable robots are designed to provide physical assistance and rehabilitation training. Light-weight designs are desirable for human usage and parallel robots are quite suitable due to low moving inertia. One of the challenges of using wearable parallel robots is to compute the end-effector position/orientation from joint angle measurements, as the forward kinematics problem is computationally difficult. It becomes even more challenging if the kinematic model changes from the nominal model due to deflection of the mechanical members, manufacturing tolerances, or misalignments of the joints between the machine and the user.Artificial neural networks have been used to provide solution of the forward kinematics problem for parallel robots. However, their efficacy has not yet been studied in wearable applications where the linkages of the robots are not fully rigid. In this paper, we conducted a case study to investigate the performance of using neural network models to compute forward kinematics of a wearable robot. Our results show that the performance of neural networks is superior to numerical approaches and produces reasonable solutions even at the boundary of the robot workspace.

This paper presents the design and preliminary evaluation of a portable spring-based knee exoskeleton, the SpringExo, which is designed to provide assistance to the leg while minimizing interference with the natural leg movement. Traditional rigid exoskeletons are unable to accurately align with a user’s anatomical joints. In addition, the user’s natural motion pattern is likely to change due to the constraints of the rigid exoskeleton. Though some textile-based soft exosuits and cable-driven soft exoskeletons have been developed to achieve better alignment with human’s biological joints, forces applied by the cables have to be sustained by human skeleton and joints. SpringExo, in comparison, uses a coil spring which the user wears around the thigh and shank, and does not require alignment with the joints. The spring stores energy and provides minimal interference during elastic deformation. A key feature of the SpringExo is that the springs store energy during the flexion phase and release this energy to assist the knee extension in the extension phase. We conducted human subjects study to verify its biomechanical and physiological effects on the user during stair ascent. Results from a six-subject study showed that the device did not interfere with the natural joint angles and assisted knee extension during stair ascent. However, further redesign and optimization are needed on the actuation system to offset SpringExo’s drawback of hindering knee flexion.

Gait training is widely used to treat gait abnormalities. Traditional gait measurement systems are limited to instrumented laboratories. Even though gait measurements can be made in these settings, it is challenging to estimate gait parameters robustly in real-time for gait rehabilitation, especially when walking over-ground. In this paper, we present a novel approach to track the continuous gait cycle during overground walking outside the laboratory. In this approach, we instrument standard footwear with a sensorized insole and an inertial measurement unit. Artificial neural networks are used on the raw data obtained from the insoles and IMUs to compute the continuous percentage of the gait cycle for the entire walking session. We show in this paper that when tested with novel subjects, we can predict the gait cycle with a Root Mean Square Error (RMSE) of 7.2%. The onset of each cycle can be detected within an RMSE time of 41.5 ms with a 99% detection rate. The algorithm was tested with 18840 strides collected from 24 adults. In this paper, we tested a combination of fully-connected layers, an Encoder-Decoder using convolutional layers, and recurrent layers to identify an architecture that provided the best performance.

For those with irregular gait, re-calibration of motor control strategies and retraining of coordination are key goals. Thoughtful external forces or resistances during repetitive tasks can reprogram motor control patterns and strategies. Prior work in our lab has utilized this theory to improve gait in various patient groups using the Tethered Pelvic Assist Device (TPAD), a treadmill-based robotic trainer. In this paper, we propose a new, portable extension of the TPAD, which relies on an open-loop, forward kinematics based controller to remove the restriction of walking in the laboratory on a treadmill, and therefore accommodates overground ambulation. To evaluate the effects of this new control scheme and the effects of the users holding the mobile TPAD frame, a dataset of walking in four conditions was collected from eight healthy individuals. When applying a constant pelvic loading force of 10% body weight, the mean ground reaction force increased by 8.2±7.7% when the individual holds the walker frame and 11.1±7.8% when no hand contact is made. The mobile TPAD was shown to still induce a targeted loading on individuals during treadmill walking. The validation of this mobile device's controller and characterization of holding the frame allow overground studies to be conducted, and now opens the door to new training paradigms for overground gait training.

Force perturbation is used in this paper to study cervical neuromuscular responses which can be used in the future to assess impairments in patients with neurological diseases. Current literature on this topic is limited to applying forces on the head in the anterior-posterior direction, perhaps due to technological limitations. In this paper, we propose to use a robotic neck brace to address these shortcomings due to its lightweight portable design and the ability to control forces. A controller is implemented to apply direction-specific perturbations on the head. To demonstrate the effectiveness of this capability, a human study was carried out with able-bodied subjects. We used this robotic brace to apply forces on the head of the subjects and observed their movement and muscle responses both when their eyes were open and closed. Our results suggest that the robotic brace is capable of perturbing the head and tracking the kinematic response. It revealed that ablebodied subjects reacted to the perturbations differently when their eyes were closed. They showed longer head trajectories and more muscle activation when the eyes were closed. We also show that the direction-specific perturbation feature enables us to analyze kinematic and muscle variables with respect to the direction of perturbation. This helps better understand the neuromuscular response in the head-neck.

Wearable robotic devices often need electrical energy. An interesting idea is to collect mechanical energy during walking and convert it into electrical energy to recharge these devices directly. In this article, we built a light-weight robotic prosthesis (1.3 kg) with the feature of self-charging. During stance phase, the prosthetic ankle joint with damping, is driven by human dynamics. The rotated ankle joint backdrives the motor, and the motor works as a generator according to the electromagnetic induction theory. Five subjects participated in experiments to verify the feasibility and five speeds walking were studied (0.7, 0.9, 1.1, and 1.3 m/s treadmill speeds and one self-selected outdoor walking speed). Experimental results demonstrate that the electrical regenerative energy per step is 1.53 ± 0.29 J on average. Meanwhile, an average consumed energy per step of the robotic prosthesis is 4.64 ± 0.15 J, which means 33 ± 5% energy can be returned to the active prosthesis (battery, 24 V, 2.6 Ah).

Adaptive cable-driven parallel robots can adjust the position of one or more pulley blocks to optimize performance within a given workspace. Because of their augmented kinematic redundancy, adaptive systems have several advantages over their traditional counterparts featuring the same numbers of cables. In this paper, we explore the application of adaptive cable-driven robots to cable-suspended camera systems. Performance of the traditional and of the adaptive designs are analyzed, using dexterity and stiffness as performance metrics. Results show superior performance of the adaptive design compared to the traditional system. An illustrative design problem for adaptive cable-suspended camera systems is also presented and solved.

Various leg exoskeletons have been designed for gait rehabilitation. The transparency of these exoskeletons is crucial to their effectiveness in gait training. The weight and inertia of an exoskeleton are two important factors affecting its transparency. In this study, using a light-weight leg exoskeleton C-ALEX, we conducted a series of experiments to explore the effect of exoskeleton weight and inertia on the natural walking of twelve healthy subjects. They walked in C-ALEX under three levels of mass added to the leg: (i) no added mass, (ii) 1.8 kg, and (iii) 3.6 kg, and three different setups of C-ALEX: (i) freewalking without C-ALEX, (ii) with C-ALEX, and (iii) with C-ALEX compensating for the weight of the added mass. The result shows that increasing exoskeleton mass increases step length, decreases step height, and reduces maximum knee flexion. After weight compensation, the step height, and the maximum knee flexion partially restored, but the step length did not, implying that the inertia is responsible for the change in step length. The study demonstrates that compensating for weight alone cannot eliminate the changes due to exoskeleton mass. On the other hand, reducing the overall mass of the exoskeleton can better preserve the natural gait of the subjects.

This paper investigates the production and identification of emotional states of a walker using plantar vibro-tactile simulations. In a first experiment, participants were asked to render, according to imagined walking scenarios, five emotions (aggressive, happy, neutral, sad, and tender) by manipulating the parameters of synthetic footstep vibrations simulating various combinations of surface materials and shoes. Results allowed to identify, for the involved emotions and vibration conditions, the mean values and ranges of variation of two parameters, vibration amplitude and temporal distance between consecutive steps. Results were in accordance with those reported in previous studies on real walking, suggesting that the plantar vibro-tactile expression of emotions in walking is independent of the real or imagined motor activity. In a second experiment, participants were asked to identify the emotions portrayed by walking vibrations synthesized by setting the synthesis engine parameters to the mean values found in the first experiment. Results showed that the involved algorithms were successful in conveying the emotional information at a level comparable with previous studies. Results of both experiments revealed strong similarities with those of an analogous study on footstep sounds suggesting that emotionally expressive walking styles are consistently produced and recognized at auditory and plantar vibro-tactile level.

As the elderly population is rapidly growing in our society, robot walking helpers are receiving more attention these days. To be practical and safe for use in daily life, an important issue is whether these robot walking helpers can be effectively maneuvered and provide guidance to the users. These concerns become even more important for a passive robot walking helper, as it relies mainly on the user's applied forces to move. In this paper, we propose a motion guidance system for a passive robot walking helper. More specifically, we develop a system to identify user's intentions from applied grip forces. This system consists of a pair of force-sensing grips attached to the handles of the robot walking helper and a learning scheme for the mapping between the measured grip forces and the driving force/torque imposed on the helper. The learning scheme, combined with an assistive strategy extended from our previous work, provides motion guidance to the elders during walking. The feasibility of the proposed system is demonstrated via a series of experiments involving motion assistance with i-Go, a passive robot walking helper developed in our laboratory.

Robotic rehabilitation devices are attractive to physical therapists. Various leg exoskeletons have been developed during the past decade and have been used in gait training. Traditional exoskeletons usually have a complex structure and add extra inertia to the wearer's leg, which may change their natural gait. In this paper, we present the design of a cable-driven active leg exoskeleton (C-ALEX) for human gait training. The advantages of cable-driven designs are that they have a simpler structure, add minimal inertia to the human limbs, and do not require precise joint alignment. C-ALEX employs the “assist-as-needed” control strategy to help the ankle center move along a prescribed path. An experiment with 6 healthy subjects was conducted who walked with C-ALEX on a treadmill. The results showed that C-ALEX is capable of helping the subjects better track a prescribed ankle path.

This paper describes the design and control architectures for a novel active thoracolumbosacral orthosis targeted at correction of abnormal postures and treatment of the human spine, often seen in adolescent idiopathic or neuromuscular scoliosis. Our novel device is motivated by the current limitations of the rigid braces used for this purpose which do not adapt to changes in the skeletal system in response to treatment. In addition, the dynamic brace can open possibilities for new treatment methods which currently do not exist. Previous brace designs were not capable of providing dynamic controlled forces. Our design utilizes two Stewart-Gough platforms in series, each controlled independently, either in position or force modes. The design can provide controlled forces/torques on different regions of spine to modify the posture. Additionally, it can control the motion of different regions of the spine through independent position control of each platform using six parallel actuators. Both control methods were validated in benchtop tests. A range of motion study was also performed with a healthy subject wearing the device while the system was controlled in transparent mode.

Aiming at the physical coupling feature between the finger and the hand exoskeleton, a human-robot interaction modeling approach is proposed. The muscle motion formulas are established based on the finger physiological structure and Hill model. The equilibrium equations between exoskeleton and finger are connected by static analysis. In order to solve the redundancy problem of the system, a method based on the physiological cross-sectional area (PCSA) is adopted to get the optimized solution of muscle force, and an optimization method based on the total minimum error (TME) is presented to obtain the parameters of Hill model. The experimental setup is established to receive the finger data of motion and force for optimization. The approach proposed can get the quantifiable muscle parameters to study the statistical analysis of muscle motion and rehabilitation state. And it will be possible for the exoskeleton and the finger to be combined as a controlled plant so as to introduce muscle parameters into the controller design.

Due to the complexity of the human musculoskeletal system and intra/intersubjects variability, powered exoskeletons are prone to human-robot misalignments. These induce undesired interaction forces that may jeopardize safe operation. Uncompensated inertia of the robotic links also generates spurious interaction forces. Current design approaches to compensate for misalignments rely on the use of auxiliary passive degrees of freedom that unavoidably increase robot inertia, which potentially affects their effectiveness in reducing undesired interaction forces. Assessing the relative impact of misalignment and robot inertia on the wearer can, therefore, provide useful insights on how to improve the effectiveness of such approaches, especially in those situations where the dynamics of the movement are quasi-periodic and, therefore, predictable such as in gait. In this paper, we studied the effects of knee joint misalignments on the wearer's gait, by using a treadmill-based exoskeleton developed by our group, the ALEX II. Knee joint misalignments were purposely introduced by adjusting the mismatch between the length of the robot thigh and that of the human thigh. The amount of robot inertia reflected to the user was adjusted through control. Results evidenced that knee misalignment significantly changes human-robot interaction forces, especially at the thigh interface, and this effect can be attenuated by actively compensating for robot inertia. Misalignments caused by an excessively long robot thigh are less critical than misalignments of equal magnitude deriving from an excessively short robot thigh.

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.

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 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 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.

This paper presents computational and experimental analyses on flight dynamics of Flapping Micro Air Vehicles (FWMAV) employing a novel flapping mechanism, denoted as AIFM (Asymmetric In-phase Flapping Mechanism). This mechanism was designed to achieve controlled, asymmetric in-phase wing flapping inspired by nature's flyers. This paper extends our previous study where modeling and optimization of such a mechanism was carried out. The dynamic effects of asymmetric in-phase flapping motion during forward flight are our main focus in this study. Kinematics and rigid body dynamics modeling are first carried out to derive the equations of motion of the system, followed by aerodynamic modeling of wing using blade element theory and quasi-unsteady analysis techniques. The analysis deals with three configurations of the system: symmetric in-phase flapping motion (C0) versus asymmetric in-phase flapping motion (C+5, C-5). Scaled model of AIFM was fabricated and implemented into a FWMAV to show its practical feasibility. Some of the key dynamic effects of AIFM are addressed, suggesting AIFM solely can generate aerodynamic forces and moments which have the potential to bring higher agility and controllability to existing FWMAV platforms.

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.

This paper introduces the overall design of ALEX III, the third generation of Active Leg Exoskeletons developed by our group. ALEX III is the first treadmill-based rehabilitation robot featuring 12 actively controlled degrees of freedom (DOF): 4 at the pelvis and 4 at each leg. As a first application of the device, we present an adaptive controller aimed to improve gait symmetry in hemiparetic subjects. The controller continuously modulates the assistive force applied to the impaired leg, based on the outputs of kernel-based non-linear filters, which learn the movements of the healthy leg. To test the effectiveness of the controller, we induced asymmetry in the gait of three young healthy subjects adding ankle weights (2.3kg). Results on kinematic data showed that gait symmetry was recovered when the controller was active.

A low-cost and easy-to-customize Cable-driven Wrist Robotic Rehabilitor (CDWRR) has been developed for forearm and wrist motion training. This device can be potentially applied to rehabilitation of stroke patients for three degree-of-freedom (3-DOF) arm motion, including forearm supination/pronation, wrist flexion/extension and ulnar/radial deviation. The CDWRR can be customized for patients with different motor impairments of the wrist. With the cable-driven parallel structure, it has properties such as low-cost, low-weight, and easy-to-reconfigure. In this paper, the structural design, kinematic analysis, workspace calculations, and parameter identification algorithms are presented. Computer simulations of the identification algorithms are performed to validate the results. Finally, preliminary experiments on a healthy subject are carried out to demonstrate the feasibility of the proposed robot to provide assistance to the human wrist and forearm during movement training.

ALEX III is a bilateral exoskeleton for gait rehabilitation. It is an evolution of two previous prototypes - ALEX and ALEX II - developed at the University of Delaware. The new robot comprises a support platform and two robotic legs. Its unique characteristic is the possibility to actively control 12 degrees-of-freedom: 4 at the pelvis and 4 for each leg. This paper focuses on the design and fabrication of the robotic leg. Results from early evaluations are presented where the robotic leg is attached to a fixed frame and controlled with a zero-interaction controller.

This paper investigates the feasibility of generating a natural looking walking gait during the swing phase for a transfemoral prosthetic leg. This prosthesis has a powered knee joint and a passive ankle joint, and is designed to be differentially flat. The diffeomorphism between the physical space and the flat output space provides a mathematical framework to solve the challenging trajectory attainment problem. The proposed methodology is demonstrated by both simulation and experiments.

Cerebral palsy (CP) is a disorder of movement and posture in children caused by non-progressive insult of the immature brain. The characteristic features are weakness, spasticity, muscle contractures, and poor motor coordination. The gait patterns of children with CP are slow, uncoordinated, and unstable. Our hypothesis is that these impaired children will benefit from robot enhanced walkers to improve their balance, coordination, and speed during gait. In addition, this experience will also impact their clinical scores that relate to their functional performance and caregiver assistance. In this study, we used a specially-designed robotic walker which children used to perform a series of walking tasks, in increasing order of difficulty. This study was performed in 30 training sessions over a period of 3 months. Each training session lasted for 20 minutes. The outcome measures were variables recorded by the robot such as travel distance, average speed, and clinical measured variables that characterize their disability profiles.

As our robotics community advances its understanding toward the optimal design of robotic exoskeletons for human gait training, the question we ask in this paper is how the anterior lunge degree of freedom in the robotic exoskeleton affects human gait training. Answering this question requires both novel robotic design and novel protocols for human gait training to characterize this effect. To the best of the authors' knowledge, this is the first study to characterize the effect of an exoskeleton's degrees of freedom on human gait adaptation. We explored this question using the Active Leg EXoskeleton (ALEX) II. The study presented was performed using ALEX II under the following two configurations: 1) locking the anterior/posterior translation in the exoskeleton, while allowing other degrees-of-freedom (labeled as locked mode) and 2) keeping the anterior/posterior degree of freedom unlocked (labeled as unlocked mode). Healthy subjects walked at self-selected speeds on a treadmill and were trained to walk with a new gait template, scaled down from their normal template. While both groups showed adaptation and retention over a 26-min period following training, the unlocked group showed better performance in terms of adaptation and retention compared with the locked group.

This paper demonstrates that for certain choices of mass distribution and addition of springs, an underactuated two-degree-of-freedom (2-DOF) \bmPRRRPsystem is static feedback linearizable, i.e., differentially flat as well. This paper is original and provides a ground breaking study in underactuated dynamical systems.

Rehabilitation robotic devices have been actively explored for training patients with impaired neural functions or assisting those with weak limbs due to aging or diseases. In recent years, the authors have proposed light-weight exoskeleton designs for the upper arm, in which rigid links of the exoskeleton are replaced by lightweight cuffs attached to the moving limb segments of the human arm. Cables, driven by motors, are routed through these cuffs to move the limb segments. However, a scientific limitation of a cable driven system is that cables can only pull but not push. Previously, the authors have demonstrated by experiments with CAREX mounted on a robotic arm that it is possible to achieve forces in all directions at the wrist. The goal of this paper is to demonstrate via experiments that CAREX is able to apply similar forces at the end-effector with healthy subjects in the device. In this research, CAREX was rigidly attached to an arm orthosis which can be tightly strapped on the human arm. The cable routing points were optimized for large “tensioned” workspace of the arm for typical Activities of Daily Living (ADLs). An orientation sensor was used to measure shoulder joint angles. Experiments are presented to validate the new sensor implementation and show the performance of CAREX on healthy subjects.

While cable-driven systems offer the advantages of being lightweight with low moving inertia, the unilateral driving property of cables generally require them to have a greater number of actuators than their rigid-linked counterparts. This paper investigates the use of springs in an attempt to reduce the number of cables required. Given an n-DOF spring-loaded cable-driven open chain, several important questions arise: (i) How can force-closure analysis be carried out for a given spring and cable routing configuration? (ii) Are n+1 cables still necessary to fully constrain the entire open chain? (iii) What is the influence of spring placement on force-closure and cable tension required? This paper will address these concerns by proposing a systematic approach based on reciprocal screw theory. The analysis shows that an n-DOF spring-loaded cable-driven open chain still requires a minimum of n+1 cables to fully constrain it. From preliminary analysis, spring placement can have a positive effect on altering the cable tension required and increasing the feasible workspace.

The thorax of an insect has direct flight muscles that can independently control the flapping amplitude, relative phase, and mean position of its left and right wings. This feature allows insects to modulate lateral dynamics during hovering flight, resulting in high flight maneuverability. This paper introduces the development and characterization of a novel flapping mechanism for MAVs, denoted as AIFM (Asymmetric In-phase Flapping Mechanism), that is capable of achieving controlled, asymmetric in-phase wing flapping as inspired by similar features in insects. The system consists of two 4-bar mechanisms that create basic flapping motions and two RRPR mechanisms that control the asymmetric flapping motion. The kinematics of the mechanism was investigated and optimized in such a way that enables the mechanism to produce reliable, in-phase wing motion during asymmetric flapping flight. The kinematics of the wings was evaluated both computationally and experimentally. It was shown that asymmetric wing flapping can be successfully achieved without affecting the in-phase flapping motion.

This paper addresses an important question in the field of rehabilitation robotics that can help engineers to develop and optimize future gait training robotic exoskeletons. This question can be posed as follows: Do the exoskeleton's degrees-of-freedom at the pelvis affect human adaptation to new gait templates? More specifically, would additional degrees-of-freedom in the exoskeleton that allow the human trunk to translate and rotate, and the hips to abduct/adduct increase human gait adaptation with an exoskeleton?

This paper investigates when a 2 degree-of-freedom PRRRP closed-chain system with a single actuator is both strongly accessible and feedback linearizable. It is demonstrated that for certain choices of mass distribution and addition of springs, an under-actuated 2 DOF PRRRP system is static feedback linearizable, i.e., also differentially flat.

Rehabilitation robots are, currently, being explored for training of neural impaired subjects or for assistance of those with weak limbs. Intensive training of neurally impaired subjects, with quantifiable outcomes, is the eventual goal of these robot exoskeletons. Conventional arm exoskeletons for rehabilitation are bulky and heavy. In recent years, the authors have proposed to make lightweight exoskeletons for rehabilitation by replacing the rigid links of the exoskeleton with lightweight cuffs fixed to the moving limb segments of the human arm. Cables are routed through these cuffs, which are driven by motors, to move the limb segments relative to each other. However, a scientific limitation of a cable-driven system is that each cable can only pull but not push. This paper is the first to demonstrate via experiments with cable-driven arm exoskeleton (CAREX) that it is possible to achieve desired forces on the hand, i.e., both pull and push, in any direction as required in neural training. In this research, an anthropomorphic arm was used to bench test the design and control concepts proposed in CAREX. As described in this paper, CAREX was attached to the limb segments of a five degree-of-freedom anthropomorphic arm instrumented with joint sensors. The cuffs of CAREX were designed to have adjustable cable routing points to optimize the “tensioned” workspace of the anthropomorphic arm. Simulation results of force field for training and rehabilitation of the arm are first presented. Experiments are conducted to show the performance of a CAREX force field controller when human subjects pull the end-effector of the anthropomorphic arm to travel on prescribed paths. The human-exoskeleton interface is also presented at the end of this paper to demonstrate the feasibility of CAREX on human arm.

It has been mathematically proven that a completely restrained n- degree-of-freedom (n-DOF) single rigid-bodied cable-driven platform requires a minimum of n + 1 cables with positive tension to fully constrain it. However, the force-closure analysis of open chains that are driven by cables is still an open question. For the case of an n -DOF cable-driven open chain, the following two important questions arise. 1) How can the force-closure analysis be carried out for a given cable routing configuration, while retaining the geometric insights of the problem? 2) Are n + 1 cables sufficient to fully constrain the entire chain? This paper addresses these issues by proposing a systematic and novel approach based on the reciprocal screw theory. The key idea is to express wrenches acting on the open chain as linear combinations of the reciprocal screws and determine the total required torques at each joint. This is followed by equating the joint torques that are provided by the cable forces with the joint torques, which are required by the external wrenches, and checking for force closure. The proposed methodology can analyze open chains with arbitrary cable routing configuration. The analysis shows that the entire n-DOF open chain requires a minimum of n + 1 cables to fully constrain it.

In contrast to a fully actuated system, an under-actuated system cannot execute all joint trajectories. However, under-actuation may be unavoidable at times, such as during joint failure. In recent literature, an under-actuated open-chain planar manipulator with revolute joints has been shown to be feedback linearizable with specific choices of mass and inertia distribution. It has been shown that the dynamic model of an n-joint manipulator with center of mass located at joint 2 and with only one actuator is static feedback linearizable if and only if the input is at the first or the last joint. In our pursuit for novel designs of under-actuated arms, which are both controllable and feedback linearizable, we investigate the feasibility of designing a 3R planar under-actuated manipulator which has a different distribution of compliance. This study shows that this new architecture of 3R planar under-actuated manipulator with one input at the second joint can still be designed to be differentially flat. With this design, a simple stabilizing controller in the flat output space enables the system to perform point-to-point motion and mitigate initial errors.

Conventional robotic rehabilitation devices for upper extremity are bulky, heavy or lack the ability to provide joint level rehabilitation. Some designs address these issues by replacing rigid links of the exoskeletons with light weight cables. However these designs are controlled in position mode instead of force control which is desirable for rehabilitation. In this paper, a 5 degree-of-freedom cable-driven upper arm exoskeleton, with control of force, is proposed. In this design, attachment points of cables on the arm are adjustable. The attachment points are optimized to achieve large workspace to perform activities of daily living. Simulation results of force field control for training and rehabilitation of the arm are presented. Experiments have been performed on a dummy robotic arm in the upper arm exoskeleton.

Due to the unilateral driving property of cables, it has been mathematically proven that a 6-DOF single rigid-bodied cable-driven platform requires a minimum of 7 cables with positive tension to fully constrain it. However, force-closure analysis of open chains driven by cables is still an open question. For the case of an n-DOF open chain driven by cables, two important questions arise: (i) Are n+1 cables sufficient to fully constrain the entire chain? (ii) How can force-closure analysis be carried out for a given cable routing configuration while retaining the geometric insights of the problem? This paper will address these issues and propose a systematic and novel approach based on the reciprocal screw theory. The analysis shows that the entire n-DOF open chain requires a minimum of n+1 cables to fully constrain it and the proposed methodology can analyze any cable routing configuration.

This work deals with the kinematic and dynamic modeling of a 3-DOF, under-actuated, pendulum-like manipulator and its control system. The cable-based device is capable of completing point-to-point planar motions, driving the end-effector from a starting pose to a goal pose, by means of two actuators only. The device relies on parametric excitation to control the oscillations of the variable-length pendulum. Unlike a previous work, the dynamic model introduced here is consistent with the assumption of cable-based device. Several control strategies are compared through numerical simulations.

In typically developing infants, the onset of crawling and walking is associated with changes across development domains such as cognition and perception ([1], [2]). Currently, infants born with significant mobility impairments do not use powered wheelchairs until three years of age [3]. This potentially limits their development in the early growth years. The goal of this research is to train infants with impairments to safely and purposefully drive a mobile robot indoors while being seated on it. We anticipate that these impaired infants will benefit from early mobility in their early years, similar to their healthy peers. Our studies with 3-12 month old infants have shown that in about six weeks of training on the mobile robot, infants can learn to drive purposefully using conventional joysticks [4]. However, they are unable to directionally control the mobile robot [5]. This poses limits on how infants can drive independently within a home environment. This paper is the first to show novel results where special needs infants learn how to make sharp turns during driving, when trained over a 5-day period with a force-feedback joystick. The joystick simulates a virtual tunnel around an intended path with turns. During training, if the infant driver moves the mobile robot outside this tunnel centered around the desired path, the driver experiences a bias corrective force on the hand. This assist-as-needed paradigm may be suitable for infant driving training and has worked well in other studies on functional training of human movements [6].

Safety is a critical issue for upper arm exoskeletons intended for human use. Joint forces and moments experienced by a human user during motion must be minimized to ensure safety. Trajectory planning and control of cable-driven exoskeletons is challenging due to the unique property that cables can transmit forces only in tension. This paper introduces the design of a 4-DOF cable-driven upper arm exoskeleton and schemes for trajectory planning and control. Simulations show that in most cases a feasible point-to-point trajectory can be generated while minimizing reaction joint forces and moments.

A large number of people suffer from impairments, such as injury to joints or the spinal cord, that limit motion of the pelvis. This motion plays an important role in balance and propulsion during a gait cycle. In this work, we present a method to design a passive device that assists the pelvis to move close to a reference trajectory during walking with partial body support. This device is un-motorized and contains only passive elements. In this paper, we model subjects with different ability levels and body weight support and determine optimum design parameters for the device. The simulation results show the configuration of the optimum device and time trajectories of pelvic rotations in comparison to the reference.

This paper discusses how mobile manipulators with an under-actuated vertical arm can be designed to be differentially flat. The property of differential flatness is achieved by appropriate inertia redistribution of the vertical arm and a wide range of under-actuation becomes possible. As a result of having the flatness property, the under-actuated mobile manipulators are capable of executing point-to-point maneuvers as mobile manipulators with a fully actuated arm would do. In addition, the trajectory planning and feedback controller design for point-to-point motions in state space is considerably simplified despite the under-actuation of the arm and nonholonomic constraints (from no-slip assumption) of the mobile base, which make the system more difficult to plan and control. These ideas are demonstrated through an illustrative example of a mobile manipulator consisting of an under-actuated vertical three-link arm and a two-wheeled differentially driven mobile base using differential flatness.

In earlier studies, the optimal wing kinematics that gives the best aerodynamic performance was determined with a robotic flapper. The geometry and physical properties of wings are also critical for designing and fabricating Flapping Wing Micro Air Vehicles (FWMAVs). In this paper, the effects of wing aspect ratio and flexibility on aerodynamic performance are experimentally investigated to determine the optimal aspect ratio for Micro Air Vehicles (MAVs) wings at Reynolds number around 18,000. The comparison between the aerodynamic performance of rigid wings and flexible wings are also made whose veins are fabricated out of different materials.

Often, electronics and packages must be prevented from damages resulting from awkward falls. The goal of this paper is to explore how actuators and control can be used to reorient bodies during free fall. It is well known that motion of a free-falling body or a set of interconnected bodies is characterized by the principle of conservation of angular momentum. The governing angular momentum equations are nonholonomic, i.e., are non-integrable rate equations. In this paper, we assume that the falling system consists of twin bodies interconnected by a hinge joint. One of the twin bodies is designated as the primary body which needs to be reoriented during fall. The secondary body is connected to the primary body by a hinge joint, similar to a protective cover on a cell phone. The relative angle between the twin bodies is actively controlled. In addition, two rotors are mounted on the primary body with axes orthogonal to the axis of the hinge between the twin bodies. The goal of this study is to use the framework of differential flatness to compute trajectories for the hinge joint and the two rotors so that the twin bodies achieve prespecified orientations at the end of the free fall.

With the growth of elderly population in our society, technology will play an important role in providing functional mobility to humans. In this paper, we propose a robot walking helper with both passive and active control modes of guidance. From the perspective of human safety, the passive mode adopts the braking control law on the wheels to differentially steer the vehicle. The active mode can guide the user efficiently when the passive control with user-applied force is not adequate for guidance. The theory of differential flatness is used to plan the trajectory of control gains within the proposed scheme of the controller. Since the user input force is not known a-priori, the theory of model predictive control is used to periodically compute the trajectory of these control gains. The simulation results show that the walking assist robot, along with the structure of this proposed control scheme, can guide the user to a goal effectively.

In this paper, we present the dynamics, control, and preliminary experiments on a wearable upper arm exoskeleton intended for human users with four degrees-of-freedom (dof), driven by six cables. The control of this cable-driven exoskeleton is complicated because the cables can transmit forces to the arm only under tension. The standard PD controllers or computed torque controllers perform only moderately since the cables need to be in tension. Future efforts will seek to refine these control strategies and their implementations to improve functionality of a human user.

Control of nonlinear under-actuated systems is an area of ongoing research. In certain applications, under- actuated systems are unavoidable. For instance, a biped can not have an actuator between the foot and the ground. In industrial robots, under-actuation can minimize cost and dead weight. Differential flatness, if applicable, provides a systematic approach to plan and control feasible trajectories for such systems. Recently, the authors have formulated a philosophy to design under-actuated planar manipulators that are differentially flat [1]. The design philosophy has two sufficient conditions: (i) an inertia distribution scheme, and (ii) an actuator and torque spring placement scheme. The philosophy covers a broad range of n-DOF manipulator designs with the degree of under- actuation varying from 1 to n - 1 as opposed to under-actuation by one or two in most of the literature on under-actuated manipulators. This paper presents a 3-DOF planar manipulator designed on the basis of this philosophy and an experimental study of controllers based on its differential flatness property. It is demonstrated experimentally that the differential flatness based controllers are able to track the desired trajectories with small tracking errors even in the presence disturbances like friction, parameter uncertainty etc. It is shown via simulation that the errors observed in the trajectories can be attributed to the friction present at the unactuated joint.

A fully actuated system can execute any joint trajectory. However, if the system is underactuated, not all joint trajectories are attainable. For such systems, it is difficult to characterize attainable joint trajectories analytically. Numerical methods are generally used to characterize these. This paper investigates the property ofdifferentialflatnessfor underactuated planar open-chain robots and studies dependence on inertia distribution within the system. It is shown that certain choices of inertia distributions make an underactuated open-chain planar robot with revolute joints feedback linearizable, i.e., also differentially flat. Once this property is established, trajectory between any two points in the state space can be planned, and a controller can be developed to correct for errors. To demonstrate the proposed methodology in hardware, experiments with an underactuated 3-DOF planar robot are also presented.

This paper describes a powered leg orthosis for gait rehabilitation of patients with walking disabilities. The paper proposes controllers which can apply suitable forces on the leg so that it moves on a desired trajectory. The description of the controllers, simulations and experimental results with the powered orthosis are presented in the paper. Currently, experiments have been performed with a dummy leg in the orthosis. In the coming months, this powered orthosis will be used on healthy subjects and stroke patients.

Gravity balancing is often used in industrial machines to decrease the required actuator efforts during motion. In this paper, we present a new design for gravity balancing of the human leg using an external orthosis. This external orthosis is connected to the human leg on the shank and its other end is fixed to a walking frame. The major issues addressed in this paper are: (i) design for gravity balancing of the human leg and the orthosis, (ii) kinematic compatibility of the human leg and the external orthosis during walking, (iii) comparison of the joint torque trajectories of the human leg with and without external orthosis, and (iv) effects of variation of the link lengths and masses of the human leg on the inertia of the external orthosis. We illustrate feasible 2D and 3D designs of the external orthosis through computer simulations. Fabrication of this design will be the subject of future work.

In this paper, we investigate design and performance of a flapping mechanism which generates flapping motion through resonant excitation similar to flight apparatus of insects. The desired flapping motion is based on optimum aerodynamic efficiency. The mechanism is driven by a conventional motor and gearbox. The rotary motion is converted into oscillatory excitation through a four-bar linkage. This study explores the optimal design parameters of this mechanism for peak performance.

In this paper, we present a passive device for swing assistance of motor-incomplete spinal cord injury patients. This device is aimed at reducing the physical demands on the therapists during treadmill training. We model the human leg as two links and a point foot mass, with a moving trunk. We employ passive elements in the design which get charged by the treadmill. Using the system dynamics, we optimize the design parameters to obtain a feasible swing motion of the leg. An exoskeleton was constructed based on these design parameters and tests were performed on a healthy subject at different treadmill speeds.

This paper considers a feedback control technique for cable suspended robots under input constraints, using control Lyapunov functions (CLF). The motivation for this work is to develop an explicit feedback control law for cable robots to asymptotically stabilize it to a goal point with positive input constraints. The main contributions of this paper are as follows: (i) proposal for a CLF candidate for a cable robot, (ii) a CLF based positive controllers for multiple inputs. An example of a three degrees-of-freedom cable suspended robot is presented to illustrate the proposed methods

In bipedal walking, a trajectory is acceptable as long as it is repetitive and allows the foot to clear the ground, while allowing the biped to move forward. Since the actual trajectory followed by a biped is not as important, a biped having more than one passive joints can also meet the motion requirements. Due to physical constraints, a biped is under-actuated at the ground contact with the feet. A biped should exhibit limit cycles when moving continuously in an environment. In general, it is difficult to prove existence of limit cycles for nonlinear systems. In this work, we generate limit cycles for a class of nonlinear underactuated bipeds using differential flatness. A specific inertia distribution renders the biped design differentially flat. Differential Flatness allows generation of a family of limit cycles amenable to numerical optimization. The results are illustrated by two DOF biped.

The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, i.e., are nonintegrable rate equations. If the base of the free-floating robot is partially actuated, it is difficult to attain trajectories of the joints that result in point-to-point motion of the entire robot system in its configuration space. However, if the drift-less system associated with the angular momentum conservation equations is shown to be differentially flat, point-to-point maneuvers of the free-floating robot in its configuration space can be constructed. However, an open research problem in the current literature is to show the property of differential flatness for a general space robot. The primary contributions of this paper are as follows: (i) study systematically the structure of the nonholonomic rate constraint equations of a free-floating open-chain space robot with arbitrarily oriented joints and two momentum wheels; (ii) establish the design conditions under which the system exhibits differential flatness; (iii) exploit these design conditions for point-to-point trajectory planning and control of the space robot

Gravity balancing of industrial robots is an important issue because these robots may have massive links in order to manipulate large payloads. In this paper, we present techniques to gravity balance the weight of moving links in industrial robots with various arrangements of joints. In a typical industrial robot, the first joint axis is parallel to the gravity vector, hence, the weight of the first moving link does not have any effect on gravity balancing of the robot. Our approach for gravity balancing of industrial robots uses two steps: (i) we locate the center of mass of distal segments of the robot using auxiliary parallelograms; (ii) we connect springs between the center of mass and other members in the robot such that the total potential energy of the system is invariant with configuration. In this paper, we present designs for gravity balancing of classes of industrial robots with revolute and prismatic joints

In this paper, we investigate designs of flapping mechanisms that allow high amplitude and high frequency of flapping. The mechanism utilizes springs and passive flapping, a concept motivated from the study of wing motion of insects and hummingbirds. The mechanisms simulate transverse bending effect of insect wings to achieve high flapping amplitudes. Different configurations of flapping mechanism are studied using dynamic simulations and quasi-steady aerodynamics. Apart from high amplitude, the results show that higher lift can be generated using these designs

In this paper, we propose a device to assist persons with hemiparesis to walk by reducing or eliminating the effects of gravity. The design of the device includes the following features: 1) it is passive, i.e., it does not include motors or actuators, but is only composed of links and springs; 2) it is safe and has a simple patient-machine interface to accommodate variability in geometry and inertia of the subjects. A number of methods have been proposed in the literature to gravity-balance a machine. Here, we use a hybrid method to achieve gravity balancing of a human leg over its range of motion. In the hybrid method, a mechanism is used to first locate the center of mass of the human limb and the orthosis. Springs are then added so that the system is gravity-balanced in every configuration. For a quantitative evaluation of the performance of the device, electromyographic (EMG) data of the key muscles, involved in the motion of the leg, were collected and analyzed. Further experiments involving leg-raising and walking tasks were performed, where data from encoders and force-torque sensors were used to compute joint torques. These experiments were performed on five healthy subjects and a stroke patient. The results showed that the EMG activity from the rectus femoris and hamstring muscles with the device was reduced by 75%, during static hip and knee flexion, respectively. For leg-raising tasks, the average torque for static positioning was reduced by 66.8% at the hip joint and 47.3% at the knee joint; however, if we include the transient portion of the leg-raising task, the average torque at the hip was reduced by 61.3%, and at the knee was increased by 2.7% at the knee joints. In the walking experiment, there was a positive impact on the range of movement at the hip and knee joints, especially for the stroke patient: the range of movement increased by 45% at the hip joint and by 85% at the knee joint. We believe that this orthosis can be potentially used to design rehabilitation protocols for patients with stroke

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. These input constraints make feedback control of cable-suspended robots a lot more challenging than their counterpart parallel-actuated robots. In this paper, we present a computationally efficient control design procedure for a cable robot with six cables, which is kinematically determined as long as all cables are in tension. The control strategy is based on dynamic aspects of statically feasible workspace. The basic idea suggested in this paper is to represent the reachable domain in terms of achievable set points under a specified control law that respects the input constraints. This computational framework is recursively used to find a set of reachable domains, using which, we are able to expand the region of feasibility by connecting adjacent domains through common points. The salient feature of the technique is that it is computationally efficient, or online implementable, for the control of a cable robot with positive input constraints. However, due to the complexity of the dynamics of general motion of a cable robot, we consider only translations. No cable interference is considered in this paper. Finally, the effectiveness of the proposed method is illustrated by numerical simulations and laboratory experiments on a six-degree-of-freedom cable-suspended robot.

In this paper, we address the design of an autopilot for autonomous landing of a helicopter on a rocking ship, due to rough sea. A tether is used for landing and securing a helicopter to the deck of the ship in rough weather. A detailed nonlinear dynamic model for the helicopter is used. This model is underactuated, where the rotational motion couples into the translation. This property is used to design controllers which separate the time scales of rotation and translation. It is shown that the tether tension can be used to couple the translation of the helicopter to the rotation. Two controllers are proposed in this paper. In the first, the rotation time scale is chosen much shorter than the translation, and the rotation reference signals are created to achieve a desired controlled behavior of the translation. In the second, due to coupling of the translation of the helicopter to the rotation through the tether, the translation reference rates are created to achieve a desired controlled behavior of the attitude and altitude. Controller A is proposed for use when the helicopter is far away from the goal, while Controller B is for the case when the helicopter is close to the ship. The proposed control schemes are proved to be robust to the tracking error of its internal loop and results in local exponential stability. The performance of the control system is demonstrated by computer simulations. Currently, work is in progress to implement the algorithm using an instrumented model of a helicopter with a tether.

In this paper, we address the design of an autopilot for autonomous landing of a helicopter on a rocking ship, due to rough sea. The deck is modeled to have a sinusoidal motion. The goal of the helicopter is to land on it during motion. In this work, we use a tether to help in target tracking. Based on the measurement of the angle between the cable and the helicopter/ship, a novel hierarchical two time-scale controller has been proposed to ensure landing of the helicopter on the ship. The system is demonstrated by computer simulation. Currently, work is under progress to implement the algorithm using an instrumented model of a helicopter using a tether.

The objective of this paper is to design a controller based on a nonlinear hover-mode model for a helicopter, which can be seamlessly integrated in an existing spatial path-planning approach. Unlike traditional approaches, this novel two-level hierarchical controller takes ‘ small-body forces’ explicitly into consideration. A higher level controller (HLC), with slower time-scale, controls the translational motion. This controller chooses the main rotor thrust, and a reference signal for the fuselage rotation matrix. This reference rotation matrix is then tracked by a lower level controller (LLC) at a faster time-scale, to select the two flapping angles of the tip path plane (TPP) and the tail rotor thrust. The reference rotation matrix is chosen by the HLC so as to meet the objective of local translation, specified by a local potential function. The local potential field is represented as an obstacle-free spherical region, a ‘ bubble’, in which the helicopter is constrained to fly. A string of such bubbles is generated by an existing spatial path-planning algorithm. The helicopter switches its controlling bubbles in a sequence to produce gross motion. The system is demonstrated by computer simulation, using a scaled model.

In this paper, navigation and control of autonomous mobile unicycle robots in a complex and partially known obstacle-ridden environment is considered. The unicycle dynamic model used has two differentially-driven wheels, with the two wheel motor torques as the system input. Two novel controllers are derived which stabilize the robot within a surrounding disk-shaped area (henceforth called a bubble) of arbitrary size for any initial velocities. The first controller takes the unicycle to the center of its bubble while the second corrects its orientation. The torque-levels can be controlled by adjusting gains. The control laws are independent of inertial parameters. An existing global planner is used by each robot to create a string of bubbles connecting its start point to its goal point, with each bubble’s size indicative of the radial obstacle-clearance available from its center. Each robot then uses its local bubble-controllers to follow its global planned path. This method is then extended to an experimental setup of multiple robots, each equipped with proximity sensors. The same algorithm is run on each robot in a distributed manner with no information sharing. Results are presented to illustrate the robustness of the system.

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.

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.

In this paper, the dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations. This model is compared with the previous models derived for similar systems. The strong accessibility condition is checked and the maximum relative degree of the system is found. Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated. The resulting equations are then used to design two novel controllers. The first one is a two-level velocity controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch (pendulum angle from the vertical) within a specified range. The second controller is also a two-level controller which stabilizes the vehicle's position to the desired point, while again keeping the pitch bounded between specified limits. Simulation results are provided to show the efficacy of the controllers using realistic data.

Gravity balancing is often used in industrial machines to decrease the actuator efforts during motion. Through the use of rehabilitation devices one can also partially balance the leg during motion with the goal to reduce net joint torque during motion. However, it is not clear as to what are the effects of such devices on legged locomotion. This paper aims to study the effect of such gravity balancing devices on the motion of bipeds during walking.

A number of methods can be found in the literature to gravity balance a machine. In this paper we use hybrid method to achieve gravity balancing. Hybrid method employs a mechanism to locate center of mass of the robot in conjunction with springs. This method is used to develop a rehabilitation device, which compensates the effect of gravity on a human leg. For a quantitative evaluation of the performance of the device, electromyograph data of the muscles involved in the motion of leg were collected and analyzed. This data showed that the machine could be used for gravity balancing of the leg and could be potentially used for rehabilitation of patients.

The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. Trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints. However, under certain conditions, these drift-less control systems can be shown to be differentially flat. The property of flatness allows a computationally inexpensive way to plan trajectories for the dynamic system between two configurations as well as develop feedback controllers. In this paper, nonholonomic rate constraints for free-floating planar open-chain robots are studied together with auxiliary joint variable constraints to determine design conditions under which the system exhibits differential flatness. Sufficient conditions are derived for existence of flatness and are illustrated by examples.

In this paper, the energetics of a flapping wing micro air vehicle is analyzed with the objective of design of flapping wing air vehicles. The salient features of this study are: (i) design of an energy storage mechanism in the air vehicle similar to an insect thorax which stores part of the kinetic energy of the wing as elastic potential energy in the thorax during a flapping cycle; (ii) inclusion of simplified aerodynamic wing models and inertia of the mechanism using rigid body modeling techniques; (iii) optimization of parameters of the energy storage mechanism using the dynamic models so that energy input from the external actuators during a flapping cycle is minimized. A series of engineering prototypes based on these studies have been fabricated which justify the use of these mathematical techniques.

Cable robots have been extensively used for the loading and unloading of cargo in shipping industries. In this paper, we look at a two-stage cable robot, i.e., a cable robot with two moving platforms connected in series. Sea conditions introduce disturbance into the system. This disturbance is considered while modeling the dynamics of the two-stage cable robot. A robust controller is designed which can assure robust tracking of the desired end-effector trajectory in the presence of the disturbance. The simulation results presented show the effectiveness of the controller.

This paper describes the dynamics and intermittent impact model of a novel rimless wheel with radially expanding spokes confined to move in a vertical plane. The wheel has two degrees of freedom, namely rotation in the plane and change of radius. The system has intermittent impacts with the ground and its mathematical model is discontinuous. The motions of the wheel on a horizontal and an inclined plane are investigated. The contact point of the wheel with the ground is assumed to have no slip. We derive the equations of motion in between the collisions and velocity change before and after the wheel impact. We construct the return map of its cyclic motion and plan the motion in between impacts to obtain a stable gait. Dynamic simulations are performed using MATLAB and are presented in the paper.

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, designs of two distinct classes of spatial robots are proposed. The designs are 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 these robots through computer simulations. Currently, we are fabricating reactionless robots to illustrate the underlying concepts.

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 online planning of the formation paths using a Dijkstra's 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-free and deadlock-free paths. Based on the feasible path for a virtual leader of the group, the trajectory planner satisfies the kinematic constraints of the individual vehicles while accounting for inter-vehicle collision and path constraints. 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 implementation with three unmanned ground vehicles are presented.

This paper addresses the problem of motion planning for free-flying robots. Full state actuation is considered to allow for large displacements of the spacecraft. Motion planning is formulated as an optimization problem and kinematic as well as dynamic constraints are considered. The chosen optimization criteria are spacecraft actuation and final time. The proposed method allows solutions which do not require any spacecraft actuation for those end goals for which the robot motion is sufficient.

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 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 describes these approaches and their effectiveness is demonstrated through simulations of a three degree-of-freedom cable suspended robots with four, five, and six cables.

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 upper arm that can fully or partially balance the human arm 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 is being 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 tailor it to an individual's needs.

This paper describes the analysis and simulation of a novel 3-wheel vehicle with expanding wheels. The motivation for this design is to attain added navigation capability by expanding the wheels according to the requirements of the terrain. For this vehicle, we present the analysis of motions in the plane and in 3D space. In these models, it is assumed that the contact point of the wheel with the ground is directly underneath the center of the wheel and has no slip. The kinematic models are studied for the property of differential flatness and this property is used to plan the trajectory and design feedback controllers. The paper presents simulations performed using MATLAB. Currently, a vehicle with these features has been fabricated at University of Delaware.

The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. It is well known that these rate constraints can also be written as input-affine drift-less control systems. Trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints. However, under certain conditions, these drift-less control systems can be shown to be differentially flat. The property of flatness allows a computationally in-expensive way to plan trajectories for the dynamic system between two configurations as well as develop feedback controllers. Nonholonomic rate constraints for free-floating planar open-chain robots are systematically studied to determine the design conditions under which the system exhibits differential flatness. Under these design conditions, the property of flatness is used for trajectory planning and feedback control under perturbations in the initial state.

For conventional robots, manipulator motions result in forces and moments on the base to cause undesirable base excitations. The objective of this paper is to systematically analyze the fundamentals of reactionless robots. Based on this analysis, design of two distinct classes of planar robots is proposed. Due to the underlying principle of conservation of angular momentum for these robots, the trajectory planning must satisfy additional constraints, illustrated through computer simulations. Currently, we are fabricating reactionless robots to illustrate the underlying concepts.

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. This feature makes the design, planning and control of cable-suspended robots a lot more challenging compared to their counterparts - parallel-actuated robots. This paper describes the kinematic and dynamic models, work-space, trajectory planning, and feedback controllers for these robots. These results are demonstrated through simulation and experiments on a six degree-of-freedom cable suspended robot.

This paper addresses the problem of trajectory planning and tracking control of groups of unmanned vehicles. The trajectory planner is aimed at satisfying the dynamic equations and constraints. The planner builds on two features of the group: (1) state equations for each member are differentially flat, and (2) inequality constraints have special structures due to proximity constraints between members. Under these assumptions, formations are made so that the dynamic equations and constraints are satisfied. Illustrative simulations of groups of unmanned ground vehicles in formations are presented. The results are also implemented on a laboratory facility with three unmanned ground vehicles.

Several studies have focussed on robotic systems with many degrees-of-freedom. Such robots often have stringent joint limits. For motion planning, a key question is to find feasible joint solutions of the system of a given position and orientation of the end-effector. In the presence of join limits, the solutions are found by searching the joint space using heuristics. In this paper, we propose a simple algorithm to construct the joint solutions for a robot chain with many degrees-of-freedom and joint limits, using dextrous workspaces. The algorithm provides a set of sufficient conditions to guarantee feasible joint solutions in the presence of limits. The procedures are illustrated by theory and experiments on PolyBot, a modular robot developed at Xerox PARC.

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 multiple degree-of-freedom structure, a single degree-of-freedom structure can be driven by a single actuator, reducing the 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.

This paper describes a prototype and analytical studies of a spherical rolling robot, a new design of a nonholonomic 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 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.

Proposes a trajectory planning scheme for open-chain systems to steer in joint space between a start and a goal, while explicitly satisfying the dynamic equations and inequality constraints prescribed in terms of joint torques, joint angles, and their higher derivatives. The algorithm consists of four steps: (i) the structure of the dynamic equations is exploited to embed the dynamic equations explicitly into the constraints; (ii) the inequalities in the space of joint angles and their derivatives are inner approximated by a set of linear inequalities, i.e., a polytope; (iii) a feasible trajectory is then sought within a class of basis functions by using a discrete collocation grid in time where the inequalities are satisfied; and (iv) the feasible trajectories are characterized in terms of a convex set of the coefficients associated with the basis functions. The approach is illustrated in theory and experiments with a master-slave dual-arm manipulation system.

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.

This paper derives two new results on optimization of nilpotent systems without drift. These results are based on the observation that nilpotent systems can be transformed into polynomial systems using product of exponential representation. Hence, the nilpotent system is first extended to become fully actuated using Lie brackets of the system vector fields with additional inputs which are fictitious. Using the product of exponential representation, this extended system is transformed to a canonical form in Phillip Hall coordinates and is well known to have a polynomial structure. The new results exploit the structure of the governing equations in Phillip Hall coordinates. These results are: 1) in the absence of inequality constraints, a quadratic cost functional in the inputs can be guaranteed to be minimized by solving a sequence of quasi-linearized problems; and 2) in the presence of state and control constraints, the optimal solution of Mayer's cost always lies on a constraint arc.

An optimal motion planning scheme for an under-actuated planar rigid body is presented. A higher-order method developed by the authors is used to construct the trajectories of this system. In this method, the explicit expressions for the states and inputs in terms of higher derivatives of a subset of states is used to change a constrained dynamic optimization problem into an unconstrained one, thereby, eliminating the need for Lagrange multipliers. The method is applied to a two input planar free-floating robot with three degrees-of-freedom and the numerical results are reported.

As robots assume more important roles in flexible manufacturing environments, they are expected to perform repeated motions while being able to quickly adapt to changes in the assembly line. It can not be ignored that the parameters of the robot influence the cost per cycle. This cost gets multiplied by the number of cycles to result in the operational cost over time. However, today, no attempts are made to design robots so that their parameters could be adjusted to the optimal values for a repeated sequence of motion. We propose a technique to identify the optimal parameters of a robot for a motion sequence between two given states in a prescribed time such that a cost functional is minimized. This proposed technique of solving this problem is new and does not use Lagrange multipliers. It is computationally efficient and the optimal parameters can be identified quickly. As a result, the parameters of a robot could be altered online in the execution of new sequences of motion.

It is quite common to see robots on assembly lines perform the same motion every sequence for long periods of time. Periodically, the robots are reprogrammed to carry out a new sequence. It can not be ignored that the parameters of the robot influence the cost per cycle. This cost is multiplied by the number of cycles to result in the operational cost over a period of time. However, today, no attempts are made to design robots so that their parameters could be adjusted to the optimal values for a given sequence of motion. In this paper, we propose a technique to identify the optimal parameters of a robot for a motion sequence between two given states in a prescribed time such that a cost functional is minimized. The proposed technique of solving this problem is new and does not use Lagrangian multiplier. It is highly computation efficient and the optimal parameters can be obtained within seconds. As a result, the parameters of a robot could be altered online as it is programmed to execute a new repetitive task.

This paper presents detailed description of a laboratory simulator that uses two robots fixed on earth to simulate the motion of a robot in space relative to a free-flying target. This simulator is appealing because it creates an environment on earth similar to what an astronaut observes watching from the space shuttle. Therefore, it could be a valuable tool for training of astronauts on earth. Also, this simulator uses off-the-shelf industrial robots in contrast to laboratory facilities today that use special designs of robots to achieve this same task. The proposed simulator can be valuable for studying real-time motion in space and in evaluating the effectiveness of onboard sensors and control systems. The objectives of this paper are to: i) describe the laboratory setup, ii) present the computational details of this simulator, iii) estimate the computation needs of this simulator, and iv) present a computer implementation of this simulator using two KUKA robots.

Freely moving systems in space conserve linear and angular momentum. As moving systems collide, the velocities get altered due to transfer of momentum. The development of strategies for assembly in a free-floating work environment requires a good understanding of primitives such as self motion of the robot, propulsion of the robot due to onboard thrusters, docking of the robot, retrieval of an object from a collection of objects, and release of an object in an object pool. The analytics of such assemblies involve not only kinematics and rigid body dynamics but also collision and impact dynamics of multibody systems. This paper presents analytical models of assembly primitives and strategies for overall assembly.>

Biological systems such as human spine, elephant trunk, snakes, and earthworms possess very high maneuverability during motion. Analogous mechanical devices are useful for applications such as inspection, exploration, manipulation, and locomotion in restricted spaces. An important feature which high mobility devices possess is small motion limits at the joints. The objectives of this paper are: (i) to present an algorithm for motion planning of planar hyper-redundant manipulator systems with limited joint motion using a discrete modal summation procedure; (ii) to apply the algorithm for motion in free space as well as retrieve objects through holes in the work environment; and (iii) to show results of application of this algorithm for motion planning of a mechanical spine with many active motion segments.>

Mathematical models are developed for the following motion primitives: (a) self-motion and -propulsion of a robot, (b) single- and dual-arm catching or release of a workpiece by a robot, and (c) catching and release of a robot chain by another robot. These primitives can be combined to build strategies for automated handling and cooperative assembly in space. The developments in this paper, even though illustrated for planar systems, easily extend to spatial free-floating robot systems.

For series chain manipulators whose links are modeled as point masses, there is a multitude of configurations in which the inertia matrix is singular. Intuitively, it is expected that these singular configurations will be complex functions of both mass centers and geometric properties of the links. It is shown that these singularities are purely geometric and can be determined by establishing linear dependence of partial velocities of the mass centers. An iterative method to find these singular configurations by working with the individual link inertia matrices as opposed to the overall inertia matrix of the chain is presented. It is believed that once an analyst is aware that the inertia matrix of a multi-degree-of freedom mechanical system can be singular, a better job of both modeling and interpreting the results of simulation can be done.>

For free-floating manipulators, the workspace of a reference point is a function of the links' geometry, the link masses, and the location of the mass centers. The question addressed is how to choose these parameters, namely, the link lengths, the link masses, and the geometric location of the mass centers such that the workspace is maximized. This question is studied for both free-floating planar open and closed chains in which all the joints are revolute.>

The following questions are addressed: how to determine the joint rates and constraints on the end-effector rates and how to know which joint rates are instantaneously inactive and which can be driven independently. The approach is based on the instantaneous properties of series chains as derived from the theory of screw systems. In this framework, those screws that correspond to the joint rates of the constituent series chains are identified. Once the correspondence is determined, the sought-after kinematic properties can be deduced from the vector space properties of these screws.>

A class of industrial tasks requires two-degree-of-freedom wrists to point an axisymmetric tool mounted at the end of a robot arm in a specified direction. Due to inherent deficiencies of wrists, such as joint limits and singular positions, the workspace of the tool on a pointing sphere is limited. A three-degree-of-freedom wrist is a redundant mechanism for point tasks. Using inverse functions, it is shown that with a redundant mechanism the workspace on the pointing sphere can be significantly improved by positioning degenerate regions at suitable areas in the workspace. The authors review arguments toward the design of an ideal redundant wrist for pointing tasks and propose an optimal modification of the wrist of an existing PUMA-560 arm. The main considerations in the modified design are existing joint limits and collisions of the total structure with the forearm. Plots of the joint angles and the joint rates in the workspace are presented. The experimental results confirm that the predicted workspace improvements are attained.>