Prescribing Cartesian Stiffness of Soft Robots by Co-Optimization of Shape and Segment-Level Stiffness.

Soft robots aim to revolutionize how robotic systems interact with the environment thanks to their inherent compliance. Some of these systems are even able to modulate their physical softness. However, simply equipping a robot with softness will not generate intelligent behaviors. Indeed, most interaction tasks require careful specification of the compliance at the interaction point; some directions must be soft and others firm (e.g., while drawing, entering a hole, tracing a surface, assembling components). On the contrary, without careful planning, the preferential directions of deformation of a soft robot are not aligned with the task. With this work, we propose a strategy to prescribe variations of the physical stiffness and the robot's posture so to implement a desired Cartesian stiffness and location of the contact point. We validate the algorithm in simulation and with experiments. To perform the latter, we also present a new tendon-driven soft manipulator, equipped with variable-stiffness segments and proprioceptive sensing and capable to move in three dimensional. We show that, combining the intelligent hardware with the proposed algorithm, we can obtain the desired stiffness at the end-effector over the workspace.

Integrating ankle and hip strategies for the stabilization of upright standing: An intermittent control model.

Even in unperturbed upright standing of healthy young adults, body sway involves concurrent oscillations of ankle and hip joints, thus suggesting to using biomechanical models with at least two degrees of freedom, namely, a double inverted pendulum (DIP) framework. However, in a previous study, it was demonstrated that the observed coordinated ankle-hip patterns do not necessarily require the independent active control of the two joints but can be explained by a simpler hybrid control system, with a single active component (intermittent, delayed sensory feedback of the ongoing sway) applied to the ankle joint and a passive component (stiffness control) applied to the hip joint. In particular, the proposed active component was based on the internal representation of a virtual inverted pendulum (VIP) that links the ankle to the current position of the global center of mass (CoM). This hybrid control system, which can also be described as an ankle strategy, is consistent with the known kinematics of the DIP and, in particular, with the anti-phase correlation of the acceleration profiles of the two joints. The purpose of this study is to extend the hybrid control model in order to apply to both the ankle and hip strategy, clarifying as well the rationale of mixed strategies. The extension consists of applying the hybrid control scheme to both joints: a passive stiffness component and an active intermittent component, based on the same feedback signals derived from the common VIP but with independent parameter gains for the two joints. Thus, the hip gains are null in the pure ankle strategy, the ankle gains are null in the pure hip strategy, and both ankle and hip gains are specifically tuned in mixed strategies. The simulation of such an extended model shows that it can reproduce both strategies; moreover, the pure ankle strategy is more robust than the hip strategy, because the range of variation (RoV) of the intermittent control gains is larger in the former case than in the latter, and the pure ankle strategy is also more energy efficient. Generally, the simulations suggest that there is no advantage to employ mixed strategies, except in borderline situations in which the control gains are just outside the RoV that provides stable control for either pure strategy: in this case, a stable mixed strategy can emerge from the combination of two marginally unstable pure strategies.

Modeling and Stiffness-based Continuous Torque Control of Lightweight Quasi-Direct-Drive Knee Exoskeletons for Versatile Walking Assistance.

State-of-the-art exoskeletons are typically limited by low control bandwidth and small range stiffness of actuators which are based on high gear ratios and elastic components (e.g., series elastic actuators). Furthermore, most exoskeletons are based on discrete gait phase detection and/or discrete stiffness control resulting in discontinuous torque profiles. To fill these two gaps, we developed a portable lightweight knee exoskeleton using quasi-direct drive (QDD) actuation that provides 14 Nm torque (36.8% biological joint moment for overground walking). This paper presents 1) stiffness modeling of torque-controlled QDD exoskeletons and 2) stiffness-based continuous torque controller that estimates knee joint moment in real-time. Experimental tests found the exoskeleton had high bandwidth of stiffness control (16 Hz under 100 Nm/rad) and high torque tracking accuracy with 0.34 Nm Root Mean Square (RMS) error (6.22%) across 0-350 Nm/rad large range stiffness. The continuous controller was able to estimate knee moments accurately and smoothly for three walking speeds and their transitions. Experimental results with 8 able-bodied subjects demonstrated that our exoskeleton was able to reduce the muscle activities of all 8 measured knee and ankle muscles by 8.60%-15.22% relative to unpowered condition, and two knee flexors and one ankle plantar flexor by 1.92%-10.24% relative to baseline (no exoskeleton) condition.

Self-Reporting Joule Heating Modulated Stiffness of Polymeric Nanocomposites for Shape Reconfiguration.

Shape reconfigurable devices, e.g., foldable phones, have emerged with the development of flexible electronics. But their rigid frames limit the feasible shapes for the devices. To achieve freely changeable shapes yet keep the rigidity of devices for user-friendly operations, stiffness-tunable materials are desired, especially under electrical control. However, current such systems are multilayer with at least a heater layer and a structural layer, leading to complex fabrication, high cost, and loss of reprocessability. Herein, we fabricate covalent adaptable networks-carbon nanotubes (CAN-CNT) composites to realize Joule heating controlled stiffness. The nanocomposites function as stiffness-tunable matrices, electric heaters, and softening sensors all by themselves. The self-reporting of softening is used to regulate the power control, and the sensing mechanism is investigated by simulating the CNT-polymer chain interactions at the nanoscale during the softening process. The nanocomposites not only have adjustable mechanical and thermodynamic properties but also are easy to fabricate at low cost and exhibit reprocessability and recyclability benefiting from the dynamic exchange reactions of CANs. Shape and stiffness control of flexible display systems are demonstrated with the nanocomposites as framing material, where freely reconfigurable shapes are realized to achieve convenient operation, wearing, or storage, fully exploiting their flexible potential.

Variable stiffness locomotion with guaranteed stability for quadruped robots traversing uneven terrains.

Quadruped robots are widely applied in real-world environments where they have to face the challenges of walking on unknown rough terrains. This paper presents a control pipeline that generates robust and compliant legged locomotion for torque-controlled quadruped robots on uneven terrains. The Cartesian motion planner is designed to be reactive to unexpected early and late contacts using the estimated contact forces. Moreover, we present a novel scheme of optimal stiffness modulation that aims to coordinate desired compliance and tracking performance. It optimizes joint stiffness and contact forces coordinately in a quadratic programming (QP) formulation, where the constraints of non-slipping contacts and torque limits are imposed as well. In addition, the issue of stability under variable stiffness control is solved by imposing a tank-based passivity constraint explicitly. We finally validate the proposed control pipeline on our quadruped robot CENTAURO in experiments on uneven terrains and, through comparative tests, demonstrate the improvements of the variable stiffness locomotion.

Materials with Electroprogrammable Stiffness.

Stiffness is a mechanical property of vital importance to any material system and is typically considered a static quantity. Recent work, however, has shown that novel materials with programmable stiffness can enhance the performance and simplify the design of engineered systems, such as morphing wings, robotic grippers, and wearable exoskeletons. For many of these applications, the ability to program stiffness with electrical activation is advantageous because of the natural compatibility with electrical sensing, control, and power networks ubiquitous in autonomous machines and robots. The numerous applications for materials with electrically driven stiffness modulation has driven a rapid increase in the number of publications in this field. Here, a comprehensive review of the available materials that realize electroprogrammable stiffness is provided, showing that all current approaches can be categorized as using electrostatics or electrically activated phase changes, and summarizing the advantages, limitations, and applications of these materials. Finally, a perspective identifies state-of-the-art trends and an outlook of future opportunities for the development and use of materials with electroprogrammable stiffness.

A Bio-Inspired Compliance Planning and Implementation Method for Hydraulically Actuated Quadruped Robots with Consideration of Ground Stiffness.

There has been a rising interest in compliant legged locomotion to improve the adaptability and energy efficiency of robots. However, few approaches can be generalized to soft ground due to the lack of consideration of the ground surface. When a robot locomotes on soft ground, the elastic robot legs and compressible ground surface are connected in series. The combined compliance of the leg and surface determines the natural dynamics of the whole system and affects the stability and efficiency of the robot. This paper proposes a bio-inspired leg compliance planning and implementation method with consideration of the ground surface. The ground stiffness is estimated based on analysis of ground reaction forces in the frequency domain, and the leg compliance is actively regulated during locomotion, adapting them to achieve harmonic oscillation. The leg compliance is planned on the condition of resonant movement which agrees with natural dynamics and facilitates rhythmicity and efficiency. The proposed method has been implemented on a hydraulic quadruped robot. The simulations and experimental results verified the effectiveness of our method.

Cascade Control of Antagonistic VSA-An Engineering Control Approach to a Bioinspired Robot Actuator.

A cascade control structure for the simultaneous position and stiffness control of antagonistic tendon-driven variable stiffness actuators (VSAs) implemented in a laboratory setup is presented in the paper. Cascade control has the ability to accelerate, additionally stabilize, and reduce oscillations, which are all extremely important in systems such as a tendon-driven compliant actuators with elastic transmission. Inner-loop controllers are closed in terms of motor positions, and outer-loop controllers in terms of actuator position and estimated stiffness. The dominant dynamics of the system (position and stiffness), composed of the mechanical part and inner loops, are identified by a closed-loop auto-regressive with exogenous input (ARX) model. The outer-loop controllers are tuned on the basis of experimentally identified transfer functions of the system in several nominal operating points for different stiffness values. After the system is identified, a controller bank is generated in which a pair of actuator position and stiffness controllers correspond to a nominal operating point and covers the area surrounding the nominal point for which it is designed. The controllers used are integral-proportional differential (I-PD) and integral-proportional (I-P) controllers, which are a variation of the PID and PI controllers with dislocated proportional and derivative gains from a direct to feedback branch that result to no overshoot for even fast reference changes (i.e., step signal), which is essential for preventing tendon slackening (meeting the pulling constraint). Analytical formulas for controller tuning based on only one parameter, λ, are also presented. Since position and stiffness loops are decoupled, it is possible to change λ for both loops independently and adjust their performance separately according to the needs. Also, the controller structure secures the smooth response without overshooting step reference or step disturbance signal, which make practical implementation possible. After all the controllers were designed, the cascade control structure for simultaneous position and stiffness control was successfully evaluated in a laboratory setup. Thus, the presented control approach is simple to implement, but with a performance that ensures a pulling constraint for tendon-driven actuators as a foundation for bioinspired antagonistic VSAs.

Development of a Virtual Force Sensor for a Low-Cost Collaborative Robot and Applications to Safety Control.

To protect operators and conform to safety standards for human-machine interactions, the design of collaborative robot arms often incorporates flexible mechanisms and force sensors to detect and absorb external impact forces. However, this approach increases production costs, making the introduction of such robot arms into low-cost service applications difficult. This study proposes a low-cost, sensorless rigid robot arm design that employs a virtual force sensor and stiffness control to enable the safety collision detection and low-precision force control of robot arms. In this design, when a robot arm is subjected to an external force while in motion, the contact force observer estimates the external torques on each joint according to the motor electric current and calculation errors of the system model, which are then used to estimate the external contact force exerted on the robot arm's end-effector. Additionally, a torque saturation limiter is added to the servo drive for each axis to enable the real-time adjustment of joint torque output according to the estimated external force, regulation of system stiffness, and achievement of impedance control that can be applied in safety measures and force control. The design this study developed is a departure from the conventional multisensor flexible mechanism approach. Moreover, it is a low-cost and sensorless design that relies on model-based control for stiffness regulation, thereby improving the safety and force control in robot arm applications.

DNA-Based Hydrogels Loaded with Au Nanoparticles or Au Nanorods: Thermoresponsive Plasmonic Matrices for Shape-Memory, Self-Healing, Controlled Release, and Mechanical Applications.

Gold nanoparticles (AuNPs) or gold nanorods (AuNRs) are loaded in polyacrylamide hydrogels cooperatively cross-linked by bis-acrylamide and nucleic acid duplexes or boronate ester-glucosamine and nucleic acid duplexes. The thermoplasmonic properties of AuNPs and AuNRs are used to control the stiffness of the hydrogels. The irradiation of the AuNP-loaded (λ = 532 nm) or the AuNR-loaded (λ = 808 nm) hydrogels leads to thermoplasmonic heating of the hydrogels, the dehybridization of the DNA duplexes, and the formation of hydrogels with lower stiffness. By ON/OFF irradiation, the hydrogels are switched between low- and high-stiffness states. The reversible control over the stiffness properties of the hydrogels is used to develop shape-memory hydrogels and self-healing soft materials and to tailor thermoplasmonic switchable drug release. In addition, by designing bilayer composites of AuNP- and AuNR-loaded hydrogels, a reversible thermoplasmonic, light-induced bending is demonstrated, where the bending direction is controlled by the stress generated in the respective bilayer composite.

A Soft-Inflatable Exosuit for Knee Rehabilitation: Assisting Swing Phase During Walking.

In this paper, we present a soft-inflatable exosuit to assist knee extension during gait training for stroke rehabilitation. The soft exosuit is designed to provide 25% of the knee moment required during the swing phase of the gait cycle and is integrated with inertial measurement units (IMUs) and smart shoe insole sensors to improve gait phase detection and controller design. The stiffness of the knee joint during level walking is computed using inverse dynamics. The soft-inflatable actuators, with an I cross-section, are mechanically characterized at varying angles to enable generation of the required stiffness outputs. A linear relation between the inflatable actuator stiffness and internal pressure as a function of the knee angle is obtained, and a two-layer stiffness controller is implemented to assist the knee joint by providing appropriate stiffness during the swing phase. Finally, to evaluate the ability of the exosuit to assist in swing motion, surface-electromyography (sEMG) sensors are placed on the three muscle groups of the quadriceps and two groups of the hamstrings, on three healthy participants. A reduction in muscle activity of the rectus femoris, vastus lateralis, and vastus medialis is observed, which demonstrates feasibility of operation and potential future usage of the soft inflatable exosuit by impaired users.

Stiffness-Controlled Thermoresponsive Hydrogels for Cell Harvesting with Sustained Mechanical Memory.

Most mechanobiological investigations focused on in situ mechanical regulation of cells on stiffness-controlled substrates with few downstream applications, as it is still challenging to harvest and expand mechanically primed cells by enzymatic digestion (e.g., trypsin) without interrupting cellular mechanical memory between passages. This study develops thermoresponsive hydrogels with controllable stiffness to generate mechanically primed cells with intact mechanical memory for augmented wound healing. No significant cellular property alteration of the fibroblasts primed on thermoresponsive hydrogels with varied stiffness has been observed through thermoresponsive harvesting. When reseeding the harvested cells for further evaluation, softer hydrogels are proven to better sustain the mechanical priming effects compared to rigid tissue culture plate, which indicates that both the stiffness-controlled substrate and thermoresponsive harvesting are required to sustain cellular mechanical memory between passages. Moreover, epigenetics analysis reveals that thermoresponsive harvesting could reduce the rearrangement and loss of chromatin proteins compared to that of trypsinization. In vivo wound healing using mechanically primed fibroblasts shows featured epithelium and sebaceous glands, which indicates augmented skin recovery compared with trypsinized fibroblasts. Thus, the thermoresponsive hydrogel-based cell harvesting system offers a powerful tool to investigate mechanobiology between cell passages and produces abundant cells with tailored mechanical priming properties for cell-based applications.

Stabilization strategies for unstable dynamics.

The stabilization of the human standing posture was originally attributed to the stiffness of the ankle muscles but direct measurements of the ankle stiffness ruled out this hypothesis, leaving open the possibility for a feedback stabilization strategy driven by proprioceptive signals. This solution, however, could be implemented with two different kinds of control mechanisms, namely continuous or intermittent feedback. The debate is now settled and the latter solution seems to be the most plausible one. Moreover, stabilization of unstable dynamics is not limited to bipedal standing. Indeed many manipulation tasks can be described in the same framework and thus a very general protocol for addressing this kind of problems is the use of haptic virtual reality where instability is generated by some kind of divergent or saddle-like force field. Several studies demonstrated that human subjects can choose to adopt a stiffness or feedback strategy as a combination of biomechanical and task constraints and can learn to switch from one strategy to the other if it is feasible or to use one or the other is infeasible. Understanding such mechanisms is relevant, for example, for the design of novel ergonomic man-machine interfaces in difficult, unstable tasks.

Distinct Inter-Joint Coordination during Fast Alternate Keystrokes in Pianists with Superior Skill.

Musical performance requires motor skills to coordinate the movements of multiple joints in the hand and arm over a wide range of tempi. However, it is unclear whether the coordination of movement across joints would differ for musicians with different skill levels and how inter-joint coordination would vary in relation to music tempo. The present study addresses these issues by examining the kinematics and muscular activity of the hand and arm movements of professional and amateur pianists who strike two keys alternately with the thumb and little finger at various tempi. The professionals produced a smaller flexion velocity at the thumb and little finger and greater elbow pronation and supination velocity than did the amateurs. The experts also showed smaller extension angles at the metacarpo-phalangeal joint of the index and middle fingers, which were not being used to strike the keys. Furthermore, muscular activity in the extrinsic finger muscles was smaller for the experts than for the amateurs. These findings indicate that pianists with superior skill reduce the finger muscle load during keystrokes by taking advantage of differences in proximal joint motion and hand postural configuration. With an increase in tempo, the experts showed larger and smaller increases in elbow velocity and finger muscle co-activation, respectively, compared to the amateurs, highlighting skill level-dependent differences in movement strategies for tempo adjustment. Finally, when striking as fast as possible, individual differences in the striking tempo among players were explained by their elbow velocities but not by their digit velocities. These findings suggest that pianists who are capable of faster keystrokes benefit more from proximal joint motion than do pianists who are not capable of faster keystrokes. The distinct movement strategy for tempo adjustment in pianists with superior skill would therefore ensure a wider range of musical expression.

Stiffness Control of Surgical Continuum Manipulators.

This paper introduces the first stiffness controller for continuum robots. The control law is based on an accurate approximation of a continuum robot's coupled kinematic and static force model. To implement a desired tip stiffness, the controller drives the actuators to positions corresponding to a deflected robot configuration that produces the required tip force for the measured tip position. This approach provides several important advantages. First, it enables the use of robot deflection sensing as a means to both sense and control tip forces. Second, it enables stiffness control to be implemented by modification of existing continuum robot position controllers. The proposed controller is demonstrated experimentally in the context of a concentric tube robot. Results show that the stiffness controller achieves the desired stiffness in steady state, provides good dynamic performance, and exhibits stability during contact transitions.