Kinematic motion planning using geometric mechanics tends to prescribe a trajectory in a parameterization of a shape space and determine its displacement in a position space. Often this trajectory is called a gait. Previous works assumed that the shape space is Euclidean when often it is not, either because the robotic joints can spin around forever (i.e., has an 𝕊 1 configuration space component, or its parameterization has an 𝕊 1 dimension). Consider a shape space that is a torus; gaits that “wrap” around the full range of a shape variable and return to its starting configuration are valid gaits in the shape space yet appear as line segments in the parameterization. Since such a gait does not form a closed loop in the parameterization, existing geometric mechanics methods cannot properly consider them. By explicitly analyzing the topology of the underlying shape space, we derive geometric tools to consider systems with toroidal and cylindrical shape spaces.

A car-like ground vehicle is a nonlinear and underactuated system subject to nonholonomic constraints. Trajectory tracking control of such systems is a challenging problem. To this end, a trajectory tracking controller based on nonlinear kinematics and dynamics model of a ground vehicle by Trajectory Tracking Control (TLC) is presented in our previous work. In this paper, we present hardware validation of TLC controller design with vehicle parameters determination for a Radio Controlled (RC) scaled model vehicle, experimental implementation, and tuning procedure. Hardware testing results are presented to demonstrate the effectiveness of our design. The design can be readily scaled-up to full-size vehicles and adapted to different types of autonomous ground vehicles with only knowledge of the vehicle model parameters.

For a lately constructed disease detection field robot, the segregation of unhealthy leaves from strawberry plants is a major task. In field operations, the picking mechanism is actuated via three previously derived inverse kinematic algorithms and their performances are compared. Due to the high risk of rapid and unexpected deviation from the target position under field circumstances, some compensation is considered necessary. For this purpose, an image-based visual servoing method via the camera-in-hand configuration is activated when the end-effector is nearby to the target leaf subsequent to performing the inverse kinematics algorithms. In this study, a bio-inspired trajectory optimization method is proposed for visual servoing and the method is constructed based on a prey-predator relationship observed in nature (“motion camouflage”). In this biological phenomenon, the predator constructs its path in a certain subspace while catching the prey. The proposed algorithm is tested both in simulations and in hardware experiments.

This paper presents the development of a piezo-based three-degree-of-freedom (3-DOF), tripedal microrobotic platform that allows for unlimited travel with sub-micron precision over a planar surface. Compliant mechanical amplifiers are incorporated with each piezoelectric stack actuator to improve both the stroke and load-bearing capability of the platform. A forward kinematic model of the stage based on its tripedal leg architecture is derived for each stick-slip step cycle and inverted for feedforward control of the platform. A prototype is constructed using low-cost 3D-printing techniques. Experimental results demonstrate actuator stroke of 29.4 μm on average with a dominant resonance of approximately 860 Hz. Results demonstrate the stage tracks a 3 mm by 3 mm square trajectory in open loop. Feedback control through visual servoing is then simulated on a model that includes flexure dynamics, observed surface interactions, and camera sampling times, reducing the root-mean-square (RMS) tracking error by 90%. This control scheme is then implemented experimentally, resulting in 99% RMS position error reduction relative to when only feedforward control is used.

This paper proposes a hybrid multibody dynamics formalism with a symbolical multibody toolbox developed in MATLAB Environment. The toolbox can generate the dynamic model of a multibody system with hybrid and nonholonomic dynamic properties. The framework and software structure of the toolbox are briefly demonstrated. The paper discusses the recursive kinematics and modular modeling theories that help improve the modeling performance and offer accessibility into the dynamic elements. The formalism that offers a symbolic solution to nonholonomic and constrained dynamics is explained in detail. The toolbox also provides design tools and auto-compilation of hybrid automata. Two exemplary models and their simulations are presented to verify the feasibility of the formalism and demonstrate the performance of the toolbox.

Developing controllers for powered prostheses is a daunting task that requires involvement from clinicians, patients and robotics experts. Difficulties arise for tuning prosthetic devices that perform in multiple conditions and provide more functionality to the user. For this reason, we propose the implementation of a simulation framework based on the open-source 3D simulation environment Gazebo, to reduce the burden of experimentation and aid in the early stages of development. In this study, we present a minimalist plugin for the simulator that allows the interfacing of a virtual model with the native prosthesis controller and renders the finding of impedance parameters as a pattern search problem. To demonstrate the functionality of this approach, we used the framework to obtain the parameters that offer the most similar joint trajectory to the respective biological counterpart during swing phase for ground level walking. The optimization results are compared against the response of a physical 2DOF knee-ankle prosthesis operating under the optimized parameters, showing congruence to our model-based results. We found that a simulation-based solution is capable of finding parameters that create an emerging behavior that approximates to the kinematic trajectory goals within a tolerance (mean absolute error ∼10%). This provides an appropriate method for development and evaluation of impedance-based controllers before deployment to the physical device.

Recent technological advancements have expanded the field of human augmentation. Specifically, lower limb exoskeletons have benefited many by providing assistance to increase mobility. The proposed study aims to develop a novel bilateral hip exoskeleton that provides mechanical power assistance in both hip flexion and extension during walking. Each actuation unit employs series elastic actuator for a high fidelity closed loop torque control utilizing a ball screw transmission incorporated with a fiberglass leaf spring. The control architecture was divided into three tiers and each tier implemented different control algorithms. The device was experimentally validated with both benchtop and human testing. Benchtop testing was done to tune required control parameters in the low-level controller and to validate the torque response. We tested five able-bodied subjects walking with our device. We analyzed their kinematic and kinetic data with different levels of mechanical power assistance during walking. Our benchtop testing results showed that the low-level PID gains were tuned to achieve desired bandwidth and torque tracking. Human testing results demonstrated that the high-level controller provided an accurate information for assistance onset timing that the hip exoskeleton was able to assist the user effectively.

The purpose of this study was to explore the effectiveness of a neural controller for a single-joint bilateral hip exoskeleton. The device provides mechanical torque in the sagittal plane and uses series elastic actuators for feedback control. The system consists of three control layers: (1) a high-level controller that estimates the current gait phase, (2) a mid-level controller that converts the electromyography (EMG) signals to desired exoskeleton torques, and (3) a low-level controller that ensures the output torque matches the commanded torque. To evaluate the effectiveness of the proportional EMG controller, one able-body subject walked with the exoskeleton under 3 assistance conditions: (1) a baseline proportional gain condition (× G ), (2) a double proportional gain condition (× 2 G ) for faster scaling, and (3) an on/off set value torque assistance ( SV ). The third condition provides the same net mechanical power as the baseline (× G ) condition to compare whether proportional scaling of the hip torque was significant. The subject’s hip-joint kinematics, metabolic rate, and muscle activities were collected as outcome measurements. In summary, the EMG controller could generate seamless torque to the user with a response time of 80 ms. The × 2 G condition resulted in a 23.3% EMG activity reduction while SV condition reduced the metabolic rate by 8.1%. Interestingly, the largest EMG reduction condition (× 2 G ) did not result in largest metabolic reduction ( SV ). Our preliminary findings suggest that the proportional scaling of the hip torque may not be the most important parameter to minimize metabolic cost.

Developing active prostheses require robust design methodologies and smart controllers in order to appropriately provide net positive mechanical work to the user. Passive prostheses are limited in their ability to sustain walking for long periods of time as well as ambulating over different terrains/environmental conditions. In this paper we present a control architecture and validation results on three individuals with transfemoral amputation using our powered knee and ankle prosthetic device. A three stage controller structure is proposed: high-level control, mid-level control, and low-level control. The high-level controller is responsible for determining the locomotion mode. At the mid-level control, an impedance controller is paired with a state machine to coordinate the kinematics and kinetics of the device with the user during community ambulation tasks. At the low-level control, the device is paired in conjunction with a series elastic actuator (SEA) at each joint to enable closed-loop torque control (PID control). Our results indicate that our powered prosthetic device is capable of scaling to a range of speeds without having to tune many impedance parameters. Our approach shows that our device is a good platform for further testing robust controllers that can provide powered assistance to the user.

Currently, wrist passive stiffness and active range of motion, two clinically relevant properties, are assessed using devices designed for rehabilitation. As a result, these devices do not have sufficient torque output and range of motion for complete wrist biomechanical assessment. To address these limitations, we are developing an actuation module specifically for assessing wrist biomechanical properties. Our device employs a serial kinematic exoskeletal architecture to directly interact with and measure wrist flexion/extension and radial/ulnar deviation. A Bowden cable-based actuation scheme, locating the motors off-board, was adopted for increased device range of motion and torque output compared with previous wrist exoskeletons. Additionally, the device was designed to incorporate a rotational elastic element at each joint, creating series elastic actuators, for accurate torque control and direct torque measurement. In this work, we present the design and demonstration of a 1-DOF module of the device, which can interact with a user’s wrist in flexion/extension, providing an important first step towards the control, evaluation, and application of the 2-DOF device.

This paper uses optimal periodic control (OPC) theory as a framework for assessing the relative efficiency of revolving versus flapping wing trajectories in insect-sized flight problems. The literature already offers both experimental and simulation-based comparisons between these two flight modes. A collective conclusion from these studies is that the potential advantages of flapping flight depend on many factors such as Reynolds number, wing size/morphology, wing kinematic constraints, aerodynamic efficiency metrics, etc. This makes it necessary to develop a unified framework for comparing these flight modes under various conditions. We address this need by using the π test from OPC theory as a tool for analyzing the degree to which one can improve the efficiency of steady rotary hovering flight through periodic trajectory perturbations. A quasi-steady insect flight model from the literature is adopted as a case study. The paper applies the π test to this model. It then concludes by solving for the optimal lift-power Pareto fronts for both flight modes, and using these Pareto fronts to confirm the results predicted by the π test.

This paper describes the design optimization of the RML Glove in order to improve its grasp performance. The existing design is limited to grasping objects of large diameter (> 110mm) due to its inability in attaining high bending angles. For an exoskeleton glove to be effective in its use as an assistive and rehabilitation device for Activities of Daily Living (ADL), it should be able to interact with objects over a wide range of sizes. Motivated by these limitations, the kinematics of the existing linkage mechanism was analyzed in detail and the design variables were identified. Two different cost functions were formulated and compared in their ability to yield optimal values for the design variables. The optimal set of design variables was chosen based on the grasp angles achieved and the resulting mechanism was simulated in CAD for feasibility testing. An exoskeleton mechanism corresponding to the index finger was manufactured with the chosen design variables and detailed experimental validation was performed to illustrate the improvement in grasp performance over the existing design. The paper ends with a summary of the experimental results and directions for future research.

Ground vehicle roll rate and pitch rate signals coming from the inertial sensors usually suffer from the drift problem: the sensor readings are slightly biased with respect to the true values. This unknown drift will have a negative impact on many control applications using these roll and pitch rate signals. This paper presents a method to estimate this drift value while the vehicle is moving, without requiring very accurate vehicle velocity or yaw rate signals. First, a few global roll and pitch angle samples are approximately estimated at some special moments during the vehicle movement. Then a linearized kinematic model is used to formulate a regression problem to estimate the drifts, given the global roll and pitch angle samples. CarSim simulation results show that the proposed method works well in both small and large drift situations.

When conducting precision operations, such as disease detection, weed removal, yield prediction, and harvesting, on plants such as strawberries and blueberries, it is necessary to know the exact location of each plant. To date, GPS and LiDAR based methods have been proposed, however these methods either cannot routinely store position data, are labor intensive, expensive, or bulky. In this study, a low cost and lightweight localization approach is proposed using relative pixel information of adjacent plants. The kinematic information of a scouting robot carrying the camera and the relative position information of adjacent plants are modeled. The centroids of strawberry plants are identified one by one via image processing technologies. An extended Kalman filter is then developed to estimate the relative positions of adjacent plants. The proposed strawberry plant localization algorithm is validated in a commercial farm. The method is low cost and can be used in routine localization operations in agricultural fields.

The paper presents method of the friction coefficient characteristics determination for kinematic pairs in the self-excited vibration conditions occurring in the Froude pendulum. Friction coefficients were calculated by measuring the vibration amplitude of the pendulum. Measurement of this amplitude for kinetic friction coefficient is carried out in the conditions of sliding friction and a static one — when the conditions of stickslip phenomena exist. The proposed method was verified using the LuGre friction model.

In this paper we present an enhanced gait emulator and a novel hybrid control system to test powered ankle-foot prostheses with two degrees of freedom in the sagittal and frontal planes. The gait emulator is a nonlinear and non-smooth system that has to follow a precisely timed set of phases to achieve a human-like periodic gait. Despite the complexity and parameter uncertainties of this five degrees of freedom system, our proposed hybrid control system simplifies the walking control by use of state triggered kinematic events. The control system works in closed loop with kinematic event detection to ensure robust and repeatable walking tests as design parameters are varied. The developed gait emulator can be used to test the prosthesis under various loading conditions and walking speeds.

Physical interaction with tools is ubiquitous in functional activities of daily living. While tool use is considered a hallmark of human behavior, how humans control such physical interactions is still poorly understood. When humans perform a motor task, it is commonly suggested that the central nervous system coordinates the musculo-skeletal system to minimize muscle effort. In this paper, we tested if this notion holds true for motor tasks that involve physical interaction. Specifically, we investigated whether humans minimize muscle forces to control physical interaction with a circular kinematic constraint. Using a simplified arm model, we derived three predictions for how humans should behave if they were minimizing muscular effort to perform the task. First, we predicted that subjects would exert workless, radial forces on the constraint. Second, we predicted that the muscles would be deactivated when they could not contribute to work. Third, we predicted that when moving very slowly along the constraint, the pattern of muscle activity would not differ between clockwise (CW) and counterclockwise (CCW) motions. To test these predictions, we instructed human subjects to move a robot handle around a virtual, circular constraint at a constant tangential velocity. To reduce the effect of forces that might arise from incomplete compensation of neuro-musculo-skeletal dynamics, the target tangential speed was set to an extremely slow pace (∼1 revolution every 13.3 seconds). Ultimately, the results of human experiment did not support the predictions derived from our model of minimizing muscular effort. While subjects did exert workless forces, they did not deactivate muscles as predicted. Furthermore, muscle activation patterns differed between CW and CCW motions about the constraint. These findings demonstrate that minimizing muscle effort is not a significant factor in human performance of this constrained-motion task. Instead, the central nervous system likely prioritizes reducing other costs, such as computational effort, over muscle effort to control physical interactions.

Quadrotor vehicles show great potential over a range of tasks, but effective control in windy environments continues to be a challenge. This paper develops a thrust-saturated controller on the Lie group SO (3) that uses flow sensing in order to reduce the effect of gusts on the vehicle. Designing the controller on SO (3) establishes almost-global exponential stability, and avoids the pitfalls of representing rigid-body kinematics using Euler angles. We prove that exponential stability is retained in the presence of thrust saturation. Aerodynamics are incorporated into the dynamics and control through a model of the blade-flapping phenomena experienced by rotorcraft. Numerical examples show that the system control remains effective despite thrust saturation, and that flow sensing improves both the initial response and steady-state error of the system in wind.

In this paper, using the Lagrange’s method a comprehensive inverse dynamics problem of a 6-3 UPS Stewart platform is investigated. First, the inverse kinematics problem is solved and the Jacobian matrix is derived. Next, the full inverse dynamics problem of the robot, taking into account the mass of links and inertia, is investigated and its governing equations are derived. The correctness of the dynamics equations are verified in two ways, first, using the results of the virtual work method and second using the results of a commercial multi-body dynamics software. Because the dynamic calculation is time consuming, two simplifying assumptions are considered. First, the link is assumed to have a zero mass and next it is assumed as a point mass. Studying the former assumption is rather straightforward. However, more complex equations are needed and derived in the present paper for the latter assumption. Required actuator forces for the two assumptions are compared with the case where the mass and link inertial is fully considered. It is shown that the first simplifying assumption significantly affects the accuracy of the required joint torques.

We propose a generalizable strategy for planning the sit to stand movement of a powered lower limb orthosis and its user. Modeling the system as a three rigid link planar robot, we rely on its kinematic equations to obtain a set of transformations that allows us to compute reference trajectories for the angular positions of the links, starting from a desired kinematic behavior for the center of mass of the robot and the angular position of link 2 relative to link 1; as we consider them more suitable to define for achieving a safe sit to stand transition. We then proceed to design a tracking controller via feedback linearization and solve a constrained least-squares program to address the control allocation problem from including the loads applied by the arms of the user as inputs. We simulate two relevant STS movements to illustrate the system tracking the reference trajectories generated with our strategy, in the presence of parameter uncertainty.