Fractional order control in haptics

Fractional order (FO) calculus—a generalization of the traditional calculus to arbitrary order differointegration-is an effective mathematical tool that broadens the modeling boundaries of the familiar integer order calculus. The effectiveness of this remarkable mathematical tool has been observed in many practical applications. For instance, FO models enable faithful representation of viscoelastic materials that exhibit frequency dependent stiffness and damping characteristics within a single mechanical element. In this dissertation, we propose and analyze the use of FO controllers in haptic systems and provide a systematic analysis of this new control method in the light of the fundamental trade-off between the stability robustness and the transparency performance. FO controllers provide a promising generalization that allows one to better shape the frequency response of a system to achieve more favorable robustness and performance characteristics. In particular, the use of FO calculus in systems and control applications provides the user with an extra design variable, the order of differointegration, which can be tuned to improve the desired behavior of the overall system. We introduce a generalized FO nondimensionalized sampled-data model for the haptic system and study its frequency dependent behaviour. Then, we analyze the stability of this system with and without a human operator in the loop. Moreover, we experimentally verify the stability analysis and demonstrate that the experiments capture the essence of the stability behaviour between different differentiation orders. The passivity analysis is conducted for two cases: the first approach takes the environment model into account and ensures the passivity of the haptic system together with the virtual environment, while the second approach assumes the presence of a passive environment model in the control loop and introduces a controller to the closed-loop system that acts like a buffer between the haptic display and the virtual environment. The second approach is more suitable for complex environments as it investigates the passivity properties of the two-port haptic system together with a virtual coupler. After characterizing the stability boundaries for the FO haptic system, we analyse the performance of the system by studying the transparency performance of the haptic rendering with such controllers. In particular, we employ effective impedance analysis to decompose the closed-loop impedance of a haptic system into its parts and study the contribution of FO elements on the stiffness and damping rendering characteristics of the system. Finally, we apply the theoretical results to a novel haptic rendering scenario: haptic rendering of viscoelastic materials. A fractional order mathematical model for the human prostate tissue with history depended stress and deflection behavior, is chosen as the viscoelastic physical system to be rendered. The stress relaxation of the haptic rendering is verified against the experimental data, indicating a high fidelity rendering

A novel approach to micro-telemanipulation with soft slave robots: integrated design of a non-overshooting series elastic actuator

Micro mechanical devices are becoming ubiquitous as they find increas- ing uses in applications such as micro-fabrication, micro-surgery and micro- probing. Use of micro-electromechanical systems not only offer compactness and precision, but also increases the efficiency of processes. Whenever me- chanical devices are used to interact with the environment, accurate control of the forces arising at the interaction surfaces arise as an important chal- lenge. In this work, we propose using a series elastic actuation (SEA) for micro- manipulation. Since an SEA is an integrated mechatronic device, the me- chanical design and controller synthesis are handled in parallel to achieve the best overall performance. The mechanical design of the μSEA is handled in two steps: type selection and dimensional synthesis. In the type selection step, a compliant, half pantograph mechanism is chosen as the underlying kinematic structure of the coupling element. For optimal dimensioning, the bandwidth of the system, the disturbance response and the force resolution are considered to achieve good control performance with high reliability. These objectives are achieved by optimizing the manipulability and the stiffness of the mechanism along with a robustness constraint. In parallel with the mechanical design, a force controller is synthesized. The controller has a cascaded structure: an inner loop for position control and an outer loop for force control. Since excess force application can be detrimental during manipulation of fragile objects; the position controller of the inner loop is designed to be a non-overshooting controller which guar- antees the force response of the system always stay lower than the reference value. This self-standing μSEA system is embedded into a 3-channel scaled tele- operation architecture so that an operator can perform micro-telemanipulation. Constant scaling between the master and the slave is implemented and the teleoperator controllers preserve the non-overshooting nature of the μSEA. Finally, the designed μSEA based micro-telemanipulation system is im- plemented and characterized

Hands-on learning with a series elastic educational robot

For gaining proficiency in physical human-robot interaction (pHRI), it is crucial for engineering students to be provided with the opportunity to physically interact with and gain hands-on experience on design and control of force-feedback robotic devices. We present a single degree of freedom educational robot that features series elastic actuation and relies on closed loop force control to achieve the desired level of safety and transparency during physical interactions. The proposed device complements the existing impedance-type Haptic Paddle designs by demonstrating the challenges involved in the synergistic design and control of admittance-type devices. We present integration of this device into pHRI education, by providing guidelines for the use of the device to allow students to experience the performance trade-offs inherent in force control systems, due to the non-collocation between the force sensor and the actuator. These exercises enable students to modify the mechanical design in addition to the controllers, by assigning different levels of stiffness values to the compliant element, and characterize the effects of these design choices on the closed-loop force control performance of the device. We also report initial evaluations of the efficacy of the device for pHRI studies

A variable-fractional order admittance controller for pHRI

In today’s automation driven manufacturing environments, emerging technologies like cobots (collaborative robots) and augmented reality interfaces can help integrating humans into the production workflow to benefit from their adaptability and cognitive skills. In such settings, humans are expected to work with robots side by side and physically interact with them. However, the trade-off between stability and transparency is a core challenge in the presence of physical human robot interaction (pHRI). While stability is of utmost importance for safety, transparency is required for fully exploiting the precision and ability of robots in handling labor intensive tasks. In this work, we propose a new variable admittance controller based on fractional order control to handle this trade-off more effectively. We compared the performance of fractional order variable admittance controller with a classical admittance controller with fixed parameters as a baseline and an integer order variable admittance controller during a realistic drilling task. Our comparisons indicate that the proposed controller led to a more transparent interaction compared to the other controllers without sacrificing the stability. We also demonstrate a use case for an augmented reality (AR) headset which can augment human sensory capabilities for reaching a certain drilling depth otherwise not possible without changing the role of the robot as the decision maker

Fractional order admittance control for physical human-robot interaction

In physical human-robot interaction (pHRI), the cognitive skill of a human is combined with the accuracy, repeatability and strength of a robot. While the promises and potential outcomes of pHRI are glamorous, the control of such coupled systems is challenging in many aspects. In this paper, we propose a new controller, fractional order admittance controller, for pHRI systems. The stability analysis of the new control system with human in-the-loop is performed and the interaction performance is investigated experimentally with 10 subjects during a task imitating a contact with a stiff environment. The results show that the fractional order controller is more robust than the standard admittance controller and helps to reduce the human effort in task execution

Multi-criteria design optimization of a compliant micro half-pantograph

This paper presents the design and the optimal dimensional synthesis of a compliant, parallel mechanism based micro gripper. Multiple design objectives are considered for the gripping task and a compliant, underactuated micro mechanism, namely a half-pantograph, is proposed as a feasible kinematic structure of the gripper. An optimization problem to study the trade-offs between multiple design criteria is formulated and dimensional synthesis of the mechanism is performed to achieve the proper directional task space stiffness of the device, while simultaneously maximizing its manipulability, using a Pareto-front based framework. An “optimal” design is selected studying the Pareto-front curve and considering the secondary design criteria

Non-overshooting force control of series elastic actuators

Whenever mechanical devices are used to interact with the environment, accurate control of the forces arising at the interaction surfaces arise as an important challenge. Traditionally, force controlled systems utilize stiff force sensors in the feedback loop to measure and regulate the interaction forces. Series elastic actuation (SEA) is an alternative approach to force control, in which the deflection of a compliant element (orders of magnitude more compliant than a typical force sensor) placed between motor and the environment is controlled to regulate the interaction forces. The use of SEAs for force control is advantageous, since this approach possesses inherent robustness without the need for high-precision force sensors/actuators and allows for accurate control of the force exerted by the actuator through position control of the deflection of a compliant coupling element. Here, a non-overshooting force controller is proposed to be embedded into the control structure of SEAs. Such a controller ensures safe operation of the SAE by making sure that the force applied to the environment is always upper bounded by the reference forces commanded to the controller

Robust optimal design of a micro gripper

This paper presents the robust optimal design of a compliant, parallel mechanism based micro gripper. Multiple design objectives are considered for the gripping task and a compliant, under-actuated micro mechanism, namely a half-pantograph, is chosen as a feasible kinematic structure of the gripper. An optimization problem to study the trade-offs between multiple design criteria is formulated and dimensional synthesis of the mechanism is performed to achieve the proper directional task space stiffness of the device, while simultaneously maximizing its manipulability, using a Pareto-front based framework. The design framework is extended by adding robustness considerations of the mechanism into the design phase. In particular, the performance of the system under variation of the design variables is analyzed using the sensitivity region concept and a family of robust Pareto-front curves are calculated. A final design is chosen from a robust Pareto-front curve based on performance threshold and a secondary design criteria that considers the torsional and unidirectional stiffness of the mechanism at the task space