Compliant Motion Research Articles

Robust adaptive impedance control of coordinated electrically driven robots: An engineering application for the (p,q)-analogue of Bernstein-Stancu operators

Function approximation techniques have emerged as influential mathematical tools for designing compliant motion controllers capable of managing objects using multiple electrical manipulators without the need for exact models. However, their effectiveness often relies on having access to velocity signals, which may not always be practical in real-world situations. This paper introduces an observer-based robust adaptive impedance control strategy that employs the (p,q)-analogue of Bernstein-Stancu operators as uncertainty estimators to tackle uncertainties in collaborative multiple electrical manipulators. This approach leverages visual task-space information and doesn’t depend on velocity feedback, enhancing cost-effectiveness and applicability in practical robotic systems. The lumped uncertainty is first modeled by this operator. The adaptation laws, derived from stability analysis, are then employed to tune its coefficients, which are not presented in the previous literature. By applying the Lyapunov lemma, the paper ensures that error signals in the controlled system are uniformly ultimately bounded (UUB). The suggested controller is evaluated in a system featuring two arms managing a rigid load. Simulation results showcase the effectiveness and versatility of the proposed approach. The outcomes are also compared with two advanced approximation techniques to demonstrate the precision and effectiveness of the suggested controller design.

Design and Self-Calibration Method of a Rope-Driven Cleaning Robot for Complex Glass Curtain Walls

Rope-driven robots are increasingly used to safely and efficiently clean complex glass curtain walls. However, continuous global cleaning is difficult for most robots because of their poor performance in overcoming obstacles and adapting to curved surfaces, and an inconvenient winch calibration on complex surfaces further burdens such work. This paper presents a 3-DOF rope-driven robot and a winch self-calibration method for efficient cleaning. The robot, by integrating a 5-rope parallel configuration, a self-adaptive cleaning body, and a self-compensating driving winch, is designed to perform continuous, compliant, and accurate spatial motion on curved walls with obstacles. By deducing the kinematic model, the constraint relationship related to orderly arranged winch positions, maneuverable body positions, and accessible rope lengths is established during the robot tracking 3D trajectory. Combining the established relationship, a series of regulations are formulated for easily acquiring body positions and rope lengths, and then a self-calibration method is proposed by accurately calculating winch positions without using professional instruments. Experimental results show that the robot can perform global and precise movement on complex glass surfaces. Applying the proposed method, the maximum winch calibration error is 6.6 mm, and the maximum body tracking error is controlled within 9.6 mm.

Compliant control of biomimetic parallel torso based on musculoskeletal control

Compliant movement and stress buffering of the torso are particularly important for state transition during high-speed locomotion in quadrupedal mammals. Currently, passive compliant control is commonly used in bionic torsos of quadruped robots, while active compliant control remains rare and immature. In previous research, we developed an active six-Degree-of-Freedom (DoF) bionic parallel torso. In this paper, we establish a muscle model that includes four biomechanical elements representing muscle characteristics (muscle force-fiber length and muscle velocity relationships) from the perspective of biology and physiology. We propose a musculoskeletal model that simulates the biological motion control system to control the compliant movement of each joint of the parallel mechanism. This model includes: 1) a neural equilibrium point controller that represents the transmission of motion commands, 2) activation dynamics that describe the activation of stimulated muscles, 3) contraction dynamics that emphasize the biomechanical characteristics of muscle tendons, 4) skeletal dynamics that describe bone movement. The effects of flexor and extensor stimulation on muscle activation, force, length, and velocity were analyzed. The results showed that both the flexor and extensor muscles will contract after corresponding stimulation. Furthermore, adjusting muscle stimulation through the musculoskeletal model can drive the parallel mechanism to reach the desired position. The musculoskeletal control method based on external force feedback can establish new torque balance in joints and drive the parallel torso to achieve compliant movements. Simulation and experiments have demonstrated the feasibility of the musculoskeletal control method. This method enhances the compliance and environmental adaptability of the parallel torso in practical applications.

A Synthesis Approach of XYZ Compliant Parallel Mechanisms Toward Motion Decoupling With Isotropic Property and Simplified Manufacturing

Abstract Decoupled compliant parallel mechanisms with isotropic legs possess many excellent performances, including ease of actuation, control, manufacture and mathematical analysis, as well as effective error compensation. Despite the advent of numerous isotropic compliant parallel mechanisms, their synthesis process predominantly relies on the empirical knowledge of engineers, with an absence of dedicated synthesis methodologies. This paper proposes the constraint algebra method, a novel synthesis method capable of autonomously exploring feasible constraint space for the synthesis. This method involves algebraic formulation of the constraints for the compliant modules, followed by solving constraint equations to find the feasible constraints and orientations, thereby facilitating the synthesis with intended performance characteristics. The multiplicity of solutions to the constraint equations enables the generation of diverse designs, including innovative configurations that are challenging to obtain via other methods and experience. Furthermore, by the consideration of machinability in several steps of synthesis, the optimal configuration can be selected for simplified manufacture. A design case has been monolithically prototyped and experimentally tested. The proposed methodology holds promise for potential extension to the synthesis of other types of compliant mechanisms.

Compliant Motion Control of Wheel-Legged Humanoid Robot on Rough Terrains

Compliant Motion Control of Wheel-Legged Humanoid Robot on Rough Terrains

Reactive bipedal balance: Coordinating compliance and stepping through virtual model imitation for enhanced stability

Compliance and step location adjustments are both important for robots to maintain balance when encountering external disturbances. Compared with controlling separately, unifying compliance with step location adjustments and integrating them into real-time pattern planning gets obvious advantages. However, the controllers’ models differ significantly from each other and from the dynamics of real position-controlled robots, compromising the stabilizing performance. In this paper, we propose a Virtual Model Imitation (VMI) strategy that unifies the controllers’ models and aligns them with actual robot dynamics. Based on this, a reactive pattern planning method is proposed which simultaneously coordinates compliance and step location adjusting strategies. The approach involves emulating the passive dynamic motion of a Linear Inverted Pendulum Model (LIPM) to enable the robot to respond to external disturbances with compliant motions automatically. Additionally, Zero Moment Point Intervened (ZI) estimation is employed to precisely determine the Center of Mass (CoM) state. Real-time optimization of step location is then conducted to stabilize the estimated CoM, actively responding to external disturbances. Importantly, the decision to adjust step location is quantitatively defined. To enhance efficiency, explicit solutions for both ZI Estimation and Step Location Optimization are provided to reduce computational costs. To validate our approach, we conducted simulations and experiments using the biped robot BHR-T, subjecting it to unexpected external pushes and obstacles during walking.

Knowledge-based self-tuning of PID control gains for continuum soft robots

In recent years, a class of soft (deformable) robots has attracted the attention of researchers due to their continuum features being advantageous over rigid robots for dexterous and safe compliant motions. These distinct advantages are obtained from the elastomer hyperelastic material properties because continuum robots are manufactured and actuated through embedded pneumatic energy fields. In this way, the continuum deformation raises novel problems in modeling and control due to its highly nonlinear behavior. That is, the deformable shape of its components varies continuously, unlike rigid robots, suggesting that the controller should compensate for its varying continuum model. Motivated by the deformable soft robot subject to parametric uncertainties and unmodeled dynamics, this paper proposes an adaptive, instead of constant, tuning of feedback gains of a model-free controller. The tuning mechanism is based on a knowledge-based scheme using a discrete wavelet neural network (DWN) by an efficient input–output identification updating its parameters and weights online, with a gradient descent algorithm driven by the identification error. At the same time, the control feedback gains are self-tuned, minimizing a convex cost function of tracking errors. Dynamic simulations show the performance of the proposed approach considering the parameters of a real soft robot mimicking a gelatin-like behavior. Finally, some discussions on the proposed scheme’s computational cost, feasibility, and viability are briefly addressed.

Reactive control of velocity fluctuations using an active deformable surface and real-time PIV

This study demonstrates an experimental realization of turbulence control strategies previously explored by Choi et al. (J. Fluid Mech., vol. 262, 1994, pp. 75–110) through numerical simulations. To conduct the experiments, a deformable surface with a streamwise array of 16 independently controlled actuators was developed. A real-time particle image velocimetry (RT-PIV) system was also created for flow measurements. The objective of the control strategy was to target the sweep and ejection motions of the vortex shedding from a spherical cap placed in a laminar boundary layer. Reactive control strategies consisted of wall-normal surface deformations that opposed or complied with the wall-normal (v) or streamwise (u) velocity fluctuations obtained from the RT-PIV. The results showed two primary outcomes of the control approach. Firstly, it effectively hindered the advancement of sweep motions towards the wall. Secondly, it disrupted the periodic shedding of vortices. The v-control with opposing wall motions and u-control with compliant wall motions exhibited strong inhibition of sweep motions, while the v-control with compliant and u-control with opposing wall motions showed weaker inhibition. All reactive control cases resulted in the disruption of vortex shedding. In some instances, this disruption was accompanied by increased turbulent kinetic energy due to the generation of additional flow motions. However, the v-control with opposing wall motions significantly reduced the vortex-shedding energy while maintaining total turbulent kinetic energy close to or below that of the unforced flow. Overall, the experiments show the effectiveness of reactive control strategies in mitigating sweep motions and disrupting vortical structures, offering insights for developing reactive control strategies.

Task-Based Compliance Control for Bottle Screw Manipulation With a Dual-Arm Robot

In this paper, a novel task-based compliance control approach for a dual-arm robot is presented with a bottle screw task. The presented approach aims at overcoming uncertainties from the object model and contact forces during the bottle screw task. A novel framework is proposed to synthesize the task motion planning and compliance control that ensure desired performance of both accuracy and compliant motion. The proposed task-based compliance control approach provides a hierarchical strategy: gross motion planning and fine compliance motion planning. The gross motion planning involves the absolute and relative motion control on a macro scale, while the fine compliance motion planning deals with uncertainties by the compliance control to accomplish a task requiring high precision robustly. A theoretical modeling of the bottle screw task is presented within the proposed framework through the analysis of uncertainties and constraints. The experimental results show that the proposed framework is efficient and robust to operate a set of bottles.

Reversible Elastomer–Fluid Transitions for Metamorphosic Robots

AbstractEndowing robots with reversible phase transition ability, especially between elastomer and fluid states, can significantly broaden their functionality and applicability. Limited attempts have been made to realize the reversible elastomer–fluid transition. Existing phase transition materials in robotics have over‐hard (≈4 GPa) or over‐soft (≈4 kPa) stiffness in the solid states, which should be further investigated to perform more compliant motions. To address these challenges, a reversible elastomer–fluid transition mechanism enabled by magnetically induced hot melt materials (MIMMs) is presented. The transition principle is explained and material characterizations are conducted. MIMMs‐based metamorphosic robots endow self‐metamorphosing abilities, such as self‐healing, spatial reshaping, self‐division/assembly, and additive manufacturability. When interacting with external environments, MIMMs‐based robots can perform further multifunctional abilities, such as collaborations for structure repairs, swimming by symbiosis with external objects, flowing through a narrow terrain by transiting to fluid, and working with elastomeric structures for stiffness‐variable fluid soft actuators. The proposed elastomer–fluid transitions open a new path for robots to generate more flexible and metamorphosic motions, thereby addressing the cross‐phase transformation challenges that soft robots face.

Task Space Compliant Control and Six-Dimensional Force Regulation Toward Automated Robotic Ultrasound Imaging

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Objective:</i> We propose a general control framework for task space compliant motion and six-dimensional (6-D) force regulation towards automated robotic ultrasound (US) imaging. The framework endows a position-controlled robotic manipulator with the capability of accurate compliant motion in free space and accurate force control in motion-constrained environment. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> An intuitive six degree-of-freedom (6-DoF) admittance control model expressed in an arbitrary Cartesian body frame is mathematically derived with closed-form task space error mapping. Its practical implementation on widely-used collaborative manipulators is proposed to achieve full task space compliant behaviors and accurate 6-D force control. A hybrid control law is presented to achieve good motion accuracy in free space and improved coupled stability in motion-constrained environment. The coupled model of physical human-robot interaction is established and the reason for the improved coupled stability is analyzed through simulation. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> Evaluation experiments on the proposed control framework were performed to show the effectiveness. The mean error of compliant trajectory following was less than 0.30 mm in free space. The mean relative force and moment control accuracy in three orthogonal directions was better than 0.5% and 0.8%, respectively. The improved coupled stability under the same model parameters was also confirmed by human-robot interaction experiments. Finally, an automated robotic US imaging experiment on a human volunteer in a real clinical scenario was carried out to show the potential application of our proposed framework. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusion:</i> Experimental results have shown the advantages of the control framework, including satisfied force control accuracy, high accuracy of compliant motion, improved coupled stability, and system effectiveness on a human volunteer. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the increasing needs of automated ultrasound (US) scanning for both diagnostic and interventional purpose. Clinical sonographers suffer from repeated workload when performing diagnostic US imaging, which could benefit from automated robotic scanning. Robotic US imaging involves physical interaction between the robot end-effector (i.e., US transducer) and the human body. The dynamics of the interaction is regulated by the control law to guarantee the contact of the US transducer and the safety of the procedure. Most existing works have focused on regulating in-plane contact force in terms of the position without considering the compliance in other dimensions. However, it is not a trivial work to extend the positional compliance to six degree-of-freedom (6-DoF) compliance. As the prevalence of low-cost collaborative robotic arms in medical scenarios, how to perform 6-DoF compliant trajectory following and accurate six-dimensional (6-D) force control on these robotic arms becomes increasingly important. This paper gives a complete general solution to achieve 6-DoF compliant control and 6-D force regulation with accurate kinematics on a position-controlled robotic arm. A hybrid control law is proposed to switch the government of “instantaneous model” and “theoretical model” to achieve compliant motion accuracy in free space and improved coupled stability in motion-constrained environment. No expensive torque sensors and torque control interface are required. And no prior geometric knowledge about the scanning object is needed. We have demonstrated the application for robotic US imaging in a real clinical scenario.

A Bimodal Hydrostatic Actuator for Robotic Legs with Compliant Fast Motion and High Lifting Force

Robotic legs, such as for lower-limb exoskeletons and prostheses, have bimodal operation: (1) within a task, like for walking (high speed and low force for the swing phase and low speed and higher force when the leg bears the weight of the system); (2) between tasks, like between walking and sit–stand motions. Sizing a traditional single-ratio actuation system for such extremum operations leads to oversized heavy electric motor and poor energy efficiency at low speeds. This paper explores a bimodal actuation concept where a hydrostatic transmission is dynamically reconfigured using custom motorized ball valves to suit the requirements of a robotic leg with a smaller and more efficient actuation system. First, this paper presents an analysis of the mass and efficiency advantages of the bimodal solution over a baseline solution, for three operating points: high-speed, high-force, and braking modes. Second, an experimental demonstration with a custom-built actuation system and a robotic leg test bench is presented. Control challenges regarding dynamic transition between modes are discussed and a control scheme solution is proposed and tested. The results show the following findings: (1) The actuator prototype can meet the requirements of a leg bimodal operation in terms of force, speed, and compliance while using smaller motors than a baseline solution. (2) The proposed operating principle and control schemes allow for smooth and fast mode transitions. (3) Motorized ball valves exhibit a good trade-off between size, speed, and flow restriction. (4) Motorized ball valves are a promising way to dynamically reconfigure a hydrostatic transmission while allowing energy to be dissipated.

Hierarchical control of manipulator with null-space compliance at the kinematic level

This article proposes a hierarchical control framework with null-space impedance at the kinematic level. The proposed framework aims to overcome the limitations of the prior methods for null-space compliance which rely on the dynamics of the manipulator. Two task-space control laws and a null-space control law at the kinematic level are designed to improve task-space errors and exhibit compliant joint motion behavior. The task-space’s end-effector force tracking uses an adaptive variable impedance control approach to enhance tracking performance. Experimental results conducted on a 7R manipulator demonstrate that the proposed control framework is capable of improving task performance when interaction forces act on the manipulator body.

A rehabilitation robot control framework with adaptation of training tasks and robotic assistance.

Robot-assisted rehabilitation has exhibited great potential to enhance the motor function of physically and neurologically impaired patients. State-of-the-art control strategies usually allow the rehabilitation robot to track the training task trajectory along with the impaired limb, and the robotic motion can be regulated through physical human-robot interaction for comfortable support and appropriate assistance level. However, it is hardly possible, especially for patients with severe motor disabilities, to continuously exert force to guide the robot to complete the prescribed training task. Conversely, reduced task difficulty cannot facilitate stimulating patients' potential movement capabilities. Moreover, challenging more difficult tasks with minimal robotic assistance is usually ignored when subjects show improved performance. In this paper, a control framework is proposed to simultaneously adjust both the training task and robotic assistance according to the subjects' performance, which can be estimated from the users' electromyography signals. Concretely, a trajectory deformation algorithm is developed to generate smooth and compliant task motion while responding to pHRI. An assist-as-needed (ANN) controller along with a feedback gain modification algorithm is designed to promote patients' active participation according to individual performance variance on completing the training task. The proposed control framework is validated using a lower extremity rehabilitation robot through experiments. The experimental results demonstrate that the control scheme can optimize the robotic assistance to complete the subject-adaptation training task with high efficiency.

Velocity observer-based robust control of piezoelectric compliant motion systems with disturbance and hysteresis estimation

This paper proposes a velocity observer-based robust control methodology for piezoelectric compliant motion systems with both unmeasurable hysteresis states and unknown disturbances. A dynamic asymmetric Bouc–Wen model is introduced to describe hysteresis behaviors of the piezoelectric compliant motion systems, a nonlinear state estimator is constructed to compensate the hysteresis nonlinearities. With the aid of the hysteresis state estimation, a velocity and disturbance observer is designed to simultaneously achieve output feedback control and disturbance rejection. Based on the estimations of the hysteresis state, the velocity, and the disturbance, a novel gain adaptation sliding mode control (SMC) structure is developed to robustly stabilize the tracking error without the requirement of velocity measurements, where the hyperbolic tangent function is employed to avoid the chattering, and the gain of the SMC is captured by an adaptive observer. By means of Lyapunov stability theory, the convergence of the hysteresis state estimation error, the velocity observation error, and the disturbance estimation error is analyzed, and the stability of such a control system is rigorously proved. Finally, the proposed control approach is applied to a piezoelectric compliant motion system without velocity sensors. The parameters of the asymmetric Bouc–Wen model are identified by using practical experimental data from the piezoelectric compliant motion system. Simulation and experimental results based on the identified model are provided to demonstrate the proposed control approach achieves excellent tracking performance with the relative error less than 0.6%. Compared with recently reported control approaches, more than 74.42% improvement on the control accuracy is confirmed in the complicated multifrequency trajectory tracking experiments.

Bioinspired Rigid-Flexible Coupled Adaptive Compliant Motion Control of Robot Gecko for Space Stations.

This paper presents a study on bioinspired rigid-flexible coupling adaptive compliant motion control of a robot gecko with hybrid actuation for space stations. The biomimetic robot gecko is made of a rigid trunk, four motor-driven active legs with dual-degree-of-freedom shoulder joints, and four pneumatic flexible pleated active attachment-detachment feet. The adaptive impedance model consists of four input parameters: the inertia coefficient, stiffness coefficient, damping coefficient, and segmented expected plantar force. The robot gecko is equipped with four force sensors mounted on its four feet, from which the normal force of each foot can be sensed in real-time. Based on the sensor signal, the variable stiffness characteristics of the feet in different states are analyzed. Furthermore, an adaptive active compliance control strategy with whole-body rigidity-flexibility-force feedback coupling is proposed for the robot gecko. Four sets of experiments are presented, including open-loop motion control, static anti-interference experiment, segmented variable stiffness experiment, and adaptative compliant motion control, both in a microgravity environment. The experiment results indicated that the presented control strategy worked well and the robot gecko demonstrates the capability of stable attachment and compliant detachment, thereby normal impact and microgravity instability are avoided. It achieves position tracking and force tracking while exhibiting strong robustness for external disturbances.

Self-adaptive rolling motion for snake robots in unstructured environments based on torque control

Snake robots have great potential for exploring and operating in challenging unstructured environments, such as rubble, caves, and narrow pipelines. However, due to the complexity and unpredictability of unstructured environments, designing a controller that can achieve adaptive motion is crucial. This paper proposes a self-adaptive torque-based rolling controller for snake robots, enabling compliant motion in unstructured environments. First, a controller is designed to modify the torque of each motor by focusing on the different motion states of the rolling gait. Second, an experimental platform is established for snake robots to verify the effectiveness of the controller. Finally, a series of rolling experiments are conducted using the torque-based rolling controller. In conclusion, the self-adaptive torque-based rolling controller enhances snake robot adaptability and mobility.

Effect of incorporating wing veins on soft wings for flapping micro air vehicles.

Small insects with flapping wings, such as bees and flies, have flexible wings with veins, and their compliant motion enhances flight efficiency and robustness. This study investigated the effects of integrating wing veins into soft wings for micro-flapping aerial vehicles. Prototypes of soft wings, featuring various wing areas and vein patterns in both the wing-chord and wing-span directions, were fabricated and evaluated to determine the force generated through flapping. The results indicated that the force is not solely dependent upon the wing area and is influenced by the wing vein pattern. Wings incorporating wing-chord veins produced more force compared to those with wing-span veins. In contrast, when the wing area was the specific wing area, wings with crossed wing veins, comprising both wing-span veins and wing-chord veins, produced more force. Although wing-chord veins tended to exert more influence on the force generated than the wing-span veins, the findings suggested that a combination of wing-span and wing-chord veins may be requisite, depending upon the wing area.

Design and test a pneumatically actuated microgripper based on structural stiffness.

In response to the problem that the actual amplification ratio of the compliant motion amplification mechanism cannot be further improved, this paper introduces a two-stage amplification microgripper based on structural stiffness that is driven by pneumatics. The mechanism not only has the advantages of good symmetry, compact structure, and large output displacement but can also reduce the relative error of the theoretical and experimental amplification ratios. The first-stage mechanism selects high-stiffness mechanisms and high-stiffness flexure hinges, and the second-stage mechanism uses low-stiffness mechanisms and low-stiffness flexure hinges. The arrangement order of the mechanism is determined by the working mode analysis. The specific dimensions of the mechanism and flexure hinges are determined through structural size optimization so that the amplification performance of the mechanism will be optimal. The experimental results show that the displacement amplification ratio of both the opening and closing of the microgripper is 41.8.

An online impedance adaptation controller for decoding skill intelligence

Variable Impedance control allows robots and humans to safely and efficiently interact with unknown external environments. This tutorial introduces online impedance adaptation control (OIAC) for variable compliant joint motions in a range of control tasks: rapid (<1s) movement control (i.e., whipping to hit), arm and finger impedance quantification, multifunctional exoskeleton control, and robot-inspired human arm control hypothesis. The OIAC has been introduced as a feedback control, which can be integrated into a feedforward control, e.g., learned by data-driven methods. This integration facilitates the understanding of human and robot arm control, closing a research loop between biomechanics and robotics. It shows not only a research way from biomechanics to robotics, but also another reserved one. This tutorial aims at presenting research examples and Python codes for advancing the understanding of variable impedance adaptation in human and robot motor control. It contributes to the state-of-the-art by providing an online impedance adaptation controller for wearable robots (i.e., exoskeletons) which can be used in robotic and biomechanical applications.