Publications

Supernumerary robotic arms have a high potential to increase human capacities to perform complicated tasks; e.g., having a third arm could increase the user’s strength, precision, reachability, and versatility. However, having a robotic manipulator working in extreme proximity to the user raises new challenges in terms of safety; i.e., uncontrolled and hazardous collisions with the user’s body parts and the environment. In this preliminary work, we show that most of these safety considerations can be extracted from standardized norms and translated into kinematics constraints for the robot. Thus, we propose a quadratic programming approach to achieve safe inverse-kinematics and physical interaction for supernumerary arms. We validate our approach in designing a safe supernumerary arm using the 7-Dof Kinova Gen3 robot.

Understanding and quantifying inter-joint coordination is valuable in several domains such as neurorehabilitation, robot-assisted therapy, robotic prosthetic arms, and control of supernumerary arms. Inter-joint coordination is often understood as a consistent spatiotemporal relation among kinematically redundant joints performing functional and goal-oriented movements. However, most approaches in the literature to investigate inter-joint coordination are limited to analysis of the end-point trajectory or correlation analysis of the joint rotations without considering the underlying task; e.g., creating a desirable hand movement toward a goal as in reaching motions. This work goes beyond this limitation by taking a model-based approach to quantifying inter-joint coordination. More specifically, we use the weighted pseudo-inverse of the Jacobian matrix and its associated null-space to explain the human kinematics in reaching tasks. We propose a novel algorithm to estimate such Inverse Kinematics weights from observed kinematic data. These estimated weights serve as a quantification for spatial inter-joint coordination; i.e., how costly a redundant joint is in its contribution to creating an end-effector velocity. We apply our estimation algorithm to datasets obtained from two different experiments. In the first experiment, the estimated Inverse Kinematics weights pinpoint how individuals change their Inverse Kinematics strategy when exposed to the viscous field wearing an exoskeleton. The second experiment shows how the resulting Inverse Kinematics weights can quantify a robotic prosthetic arm’s contribution (or the level of assistance).

Many human-robot collaboration scenarios can be seen as a redundant leader-follower setup where the human (i.e., the leader) can potentially perform the task without the assistance of the robot (i.e., the follower). Thus, the goal of the collaboration, beside stable execution of the task, is to reduce the human cost; e.g., ergonomic, or cognitive cost. Such system redundancies (where the same task be achieved in different manner) can also be exploited as a communication channel for the human to convey his/her intention to the robot; since it is essential for the overall performance (both execution and assistance) that the follower recognizes the intended task in an online fashion. Having an estimation for the intended task, the robot can assist the human by reducing the human cost over the task null-space; i.e., the null-space which arises from the overall system redundancies with respect to the intended task. With the prospective of supernumerary and prosthetic robots, in this work, we primarily focus on serial manipulation in which the proximal/distal part of the kinematic chain is controlled by the leader/follower respectively. By exploiting kinematic redundancies for intention-recognition and costminimization, our proposed control strategy (for the follower) ensures assistance under stable execution of the task. Our results (simulations and preliminary experimentation) show the efficacy of our method in providing a seamless robotic assistance (i.e., improving human posture) toward human intended tasks (i.e., reaching motions) for wearable robotics.

A seamless interaction requires two robotic behaviors: the leader role where the robot rejects the external perturbations and focuses on the autonomous execution of the task, and the follower role where the robot ignores the task and complies with human intentional forces. The goal of this work is to provide (1) a unified robotic architecture to produce these two roles, and (2) a human-guidance detection algorithm to switch across the two roles. In the absence of human-guidance, the robot performs its task autonomously and upon detection of such guidances the robot passively follows the human motions. We employ dynamical systems to generate task-specific motion and admittance control to generate reactive motions toward the human-guidance. This structure enables the robot to reject undesirable perturbations, track the motions precisely, react to human-guidance by providing proper compliant behavior, and re-plan the motion reactively. We provide analytical investigation of our method in terms of tracking and compliant behavior. Finally, we evaluate our method experimentally using a 6-DoF manipulator.

Many manipulation tasks require coordinated motions for arm and fingers. Complexity increases when the task requires to control for the force at contact against a non-flat surface; This becomes even more challenging when this contact is done on a human. All these challenges are regrouped when one, for instance, massages a human limb. When massaging, the robotic arm is required to continuously adapt its orientation and distance to the limb while the robot fingers exert desired patterns of forces and motion on the skin surface. To address these challenges, we adopt a Dynamical System (DS) approach that offers a unified motion-force control approach and enables to easily coordinate multiple degrees of freedom. As each human limb may slightly differ, we learn a model of the surface using support vector regression (SVR) which enable us to obtain a distance-to-surface mapping. The gradient of this mapping, along with the DS, generates the desired motions for the interaction with the surface. A DS-based impedance control for the robotic fingers allows to control separately for force along the normal direction of the surface while moving in the tangential plane. We validate our approach using the KUKA IIWA robotic arm and Allegro robotic hand for massaging a mannequin arm covered with a skin-like material.We show that our approach allows for 1) reactive motion planning to reach for an unknown surface, 2) following desired motion patterns on the surface, and 3) exerting desired interaction forces profiles. Our results show the effectiveness of our approach; especially the robustness toward uncertainties for shape and the given location of the surface.

In many tasks such as finishing operations, achieving accurate force tracking is essential. However, uncertainties in the robot dynamics and the environment limit the force tracking accuracy. Learning a compensation model for these uncertainties to reduce the force error is an effective approach to overcome this limitation. However, this approach requires an adaptive and robust framework for motion and force generation. In this paper, we use the time-invariant Dynamical System (DS) framework for force adaptation in contact tasks. We propose to improve force tracking accuracy through online adaptation of a state-dependent force correction model encoded with Radial Basis Functions (RBFs). We evaluate our method with a KUKA LWR IV+ robotic arm. We show its efficiency to reduce the force error to a negligible amount with different target forces and robot velocities. Furthermore, we study the effect of the hyper-parameters and provide a guideline for their selection. We showcase a collaborative cleaning task with a human by integrating our method to previous works to achieve force, motion, and task adaptation at the same time. Thereby, we highlight the benefits of using adaptive force control in real-world environments where we need reactive and adaptive behaviours in response to interactions with the environment.

Assistive robotics aims to design physically collaborative robots which are able to help human partners with cumbersome tasks; for instance, lifting a heavy plank/guard and inserting it into a frame at the ceiling. To reduce human loadshare, it is expected from the robot to perform such tasks in coordination with the human partner. Uncertainty of human behavior and complex dynamics of real-world environments pose challenging problems for robotic systems. It is crucial to employ control frameworks that allow for both motion tracking and interaction/force control. Furthermore, the framework should allow for reactive and adaptive motion planning toward human behavior. To deliver these requirements, we propose a Dynamical System-based control architecture with adaptation capabilities. Our preliminary experimentation using ARMAR6 shows promising performances to achieve such a complex task in collaboration with human users.

Many tasks require the robot to enter in contact with surfaces, be it to take support, to polish or to grasp an object. It is crucial that the robot controls forces both upon making contact and while in contact. While many solutions exist to control for contact, none offer the required robustness to adapt to real-world uncertainties, such as sudden displacement of the object prior and once in contact. To adapt to such disturbances require to re-plan on the fly both the trajectory and the force. Dynamical systems (DS) offer a framework for instant re-planning of trajectories. They are however limited to control of motions. We extend this framework here to enable generating contact forces and trajectories through DS. The framework allows also to modulate the impedance so as to show rigidity to maintain contact, and compliance to ensure safe interaction with humans. We validate the approach in single and dual arm setting using KUKA LWR 4+ robotic arms. We show that the approach allows 1) to make smooth contact while applying large forces, 2) to maintain desired contact force when scanning non-linear surfaces, even when the surface is moved, and 3) to grasp and lift smoothly an object in the air, and to re-balance forces on the fly to maintain the grasp even when subjected to strong external disturbances.

Social robotic assistants have been widely studied and deployed as telepresence tools or caregivers. Evaluating their design and impact on the people interacting with them is of prime importance. In this research, we evaluate the usability and impact of ARMAR-6, an industrial robotic assistant for maintenance tasks. For this evaluation, we have used a modified System Usability Scale (SUS) to assess the general usability of the robotic system and the Godspeed questionnaire series for the subjective perception of the coworker. We have also recorded the subjects’ gaze fixation patterns and analyzed how they differ when working with the robot compared to a human partner.

The goal of this work is to enable robots to intelligently and compliantly adapt their motions to the intention of a human during physical Human–Robot Interaction in a multi-task setting. We employ a class of parameterized dynamical systems that allows for smooth and adaptive transitions between encoded tasks. To comply with human intention, we propose a mechanism that adapts generated motions (i.e., the desired velocity) to those intended by the human user (i.e., the real velocity) thereby switching to the most similar task. We provide a rigorous analytical evaluation of our method in terms of stability, convergence, and optimality yielding an interaction behavior which is safe and intuitive for the human. We investigate our method through experimental evaluations ranging in different setups: a 3-DoF haptic device, a 7-DoF manipulator and a mobile platform.

The use of humanoid robots to play a therapeutic role in helping individuals with social disorders such as autism is a newly emerging field, but remains unexplored in schizophrenia. As the ability for robots to convey emotion appear of fundamental importance for human-robot interactions, we aimed to evaluate how schizophrenia patients recognize positive and negative facial emotions displayed by a humanoid robot. We included 21 schizophrenia outpatients and 17 healthy participants. In a reaction time task, they were shown photographs of human faces and of a humanoid robot (iCub) expressing either positive or negative emotions, as well as a non-social stimulus. Patients’ symptomatology, mind perception, reaction time and number of correct answers were evaluated. Results indicated that patients and controls recognized better and faster the emotional valence of facial expressions expressed by humans than by the robot. Participants were faster when responding to positive compared to negative human faces and inversely were faster for negative compared to positive robot faces. Importantly, participants performed worse when they perceived iCub as being capable of experiencing things (experience subscale of the mind perception questionnaire). In schizophrenia patients, negative correlations emerged between negative symptoms and both robot’s and human’s negative face accuracy. Individuals do not respond similarly to human facial emotion and to non-anthropomorphic emotional signals. Humanoid robots have the potential to convey emotions to patients with schizophrenia, but their appearance seems of major importance for human-robot interactions.

The goal of this work is to enable robots to intelligently and compliantly adapt their motions to the intention of a human during physical Human-Robot Interaction (pHRI) in a multi-task setting. We employ a class of parameterized dynamical systems that allows for smooth and adaptive transitions across encoded tasks. To comply with human intention, we propose a mechanism that adapts generated motions (i.e., the desired velocity) to those intended by the human user (i.e., the real velocity) thereby switching to the most similar task. We investigate our method through experimental evaluations for different robotic scenarios.

In this work, we present an adaptive motion planning approach for impedance-controlled robots to modify their tasks based on human physical interactions. We use a class of parameterized time-independent dynamical systems for motion generation where the modulation of such parameters allows for motion flexibility. To adapt to human interactions, we update the parameters of our dynamical system in order to reduce the tracking error (i.e., between the desired trajectory generated by the dynamical system and the real trajectory influenced by the human interaction). We provide analytical analysis and several simulations of our method. Finally, we investigate our approach through real world experiments with a 7-DOF KUKA LWR 4+ robot performing tasks such as polishing and pick-and-place.

We present novel, low-cost and non-invasive potential diagnostic biomarkers of schizophrenia. They are based on the ‘mirror-game’, a coordination task in which two partners are asked to mimic each other’s hand movements. In particular, we use the patient’s solo movement, recorded in the absence of a partner, and motion recorded during interaction with an artificial agent, a computer avatar or a humanoid robot. In order to discriminate between the patients and controls, we employ statistical learning techniques, which we apply to nonverbal synchrony and neuromotor features derived from the participants’ movement data. The proposed classifier has 93% accuracy and 100% specificity. Our results provide evidence that statistical learning techniques, nonverbal movement coordination and neuromotor characteristics could form the foundation of decision support tools aiding clinicians in cases of diagnostic uncertainty.

Rapid progress in the area of humanoid robots offers tremendous possibilities for investigating and improving social competences in people with social deficits, but remains yet unexplored in schizophrenia. In this study, we examined the influence of social feedbacks elicited by a humanoid robot on motor coordination during a human-robot interaction. Twenty-two schizophrenia patients and twenty-two matched healthy controls underwent a collaborative motor synchrony task with the iCub humanoid robot. Results revealed that positive social feedback had a facilitatory effect on motor coordination in the control participants compared to non-social positive feedback. This facilitatory effect was not present in schizophrenia patients, whose social-motor coordination was similarly impaired in social and non-social feedback conditions. Furthermore, patients’ cognitive flexibility impairment and antipsychotic dosing were negatively correlated with patients’ ability to synchronize hand movements with iCub. Overall, our findings reveal that patients have marked difficulties to exploit facial social cues elicited by a humanoid robot to modulate their motor coordination during human-robot interaction, partly accounted for by cognitive deficits and medication. This study opens new perspectives for comprehension of social deficits in this mental disorder.

We present a novel adaptive oscillator, called Adaptive Natural Oscillator (ANO), to exploit the natural dynamics of a given robotic system. This tool is built upon the Adaptive Frequency Oscillator (AFO), and it can be used as a pattern generator in robotic applications such as locomotion systems. In contrast to AFO, that adapts to the frequency of an external signal, ANO adapts the frequency of reference trajectory to the natural dynamics of the given system. In this work, we prove that, in linear systems, ANO converges to the system’s natural frequency. Furthermore, we show that this tool exploits the natural dynamics for energy efficiency through minimization of actuator effort. This property makes ANO an appealing tool for energy consumption reduction in cyclic tasks; especially in legged systems. We also extend the proposed adaptation mechanism to high dimensional and general cases; such as -DOF manipulators. In addition, by investigating a hopper leg in simulation, we show the efficacy of ANO in face of dynamical discontinuities; such as those inherent in legged locomotion. Furthermore, we apply ANO to a simulated compliant robotic manipulator performing a periodic task where the energy consumption is drastically reduced. Finally, the experimental results on a -DOF compliant joint show that our adaptive oscillator, despite all practical uncertainties and deviations from theoretical models, exploits the natural dynamics and reduces the energy consumption.

Schizophrenia patients are known to be impaired in their ability to process social information and to engage in social interactions. To understand better social cognition in schizophrenia, we investigate the links between these impairments. In this paper, we focus primarily on the influence of social feedback, such as facial emotions, on motor coordination during joint action. To investigate and quantify this influence, we exploited systematically-controlled social and nonsocial feedback provided by a humanoid robot. Humanoid robotics technology offers interactive designs and can precisely control the properties of the feedback provided during the interaction. In this work, a joint-action task with a robot is performed to investigate how social cognition is affected by cognitive capabilities and symptomatology. Results show that positive social feedback has a facilitatory effect on social-motor coordination in the control participants compared to nonsocial positive feedback. This facilitation effect is not present in schizophrenia patients, whose social-motor coordination is similar in social and nonsocial feedback conditions. This result is strongly correlated with performances in the Trail Making Test (TMT), which highlights the link between cognitive deficits and social-motor coordination in schizophrenia.

We present a compliance adaptation method for online natural dynamics modification of multi-joint robots performing cyclic tasks. In this method, parameters of multi-basis nonlinear compliances, acting in parallel with actuators, are adapted to minimize actuation forces which results in joint-byjoint energy consumption reduction. Stability, convergence, and optimality of this method are proved analytically for a general compliance structure. We do not impose any specific constraint on the controller structure and tracking performance, yet stable tracking of cyclic motions is necessary for the convergence to the optimal solution. Extensive simulations on a set of systems, ranging from simple mass-spring system to robotic manipulator (with linear and nonlinear compliances), along with the experimental results on a 1-DOF compliant revolute joint with two basis functions in the compliance profile, demonstrate the efficiency of our method in terms of stability, convergence, and optimality; i.e., actuation force and energy consumption reduction.

Catching a fast flying object is particularly challenging as it consists of two tasks: extremely precise estimation of the object’s motion and control of the robot’s motion. Any small imprecision may lead the fingers to close too abruptly and let the object fly away from the hand before closing. We present a strategy to overcome for sensorimotor imprecision by introducing softness in the catching approach. Soft catching consists of having the robot moves with the object for a short period of time, so as to leave more time for the fingers to close on the object. We use a dynamic system-based control law to generate the appropriate reach and follow motion, which is expressed as a linear parameter varying (LPV) system. We propose a method to approximate the parameters of LPV systems using Gaussian mixture models, based on a set of kinematically feasible demonstrations generated by an offline optimal control framework. We show theoretically that the resulting DS will intercept the object at the intercept point, at the right time with the desired velocity direction. Stability and convergence of the approach are assessed through Lyapunov stability theory. The proposed method is validated systematically to catch three objects that generate elastic contacts and demonstrate important improvement over a hard catching approach.

The use of humanoid robots to play a therapeutic role in helping individuals with social disorders such as autism is a newly emerging field, but remains unexplored in schizophrenia. As the ability for robots to convey emotion appear of fundamental importance for human-robot interactions, we aimed to evaluate how schizophrenia patients recognize positive and negative facial emotions displayed by a humanoid robot. We included 21 schizophrenia outpatients and 17 healthy participants. In a reaction time task, they were shown photographs of human faces and of a humanoid robot (iCub) expressing either positive or negative emotions, as well as a non-social stimulus. Patients’ symptomatology, mind perception, reaction time and number of correct answers were evaluated. Results indicated that patients and controls recognized better and faster the emotional valence of facial expressions expressed by humans than by the robot. Participants were faster when responding to positive compared to negative human faces and inversely were faster for negative compared to positive robot faces. Importantly, participants performed worse when they perceived iCub as being capable of experiencing things (experience subscale of the mind perception questionnaire). In schizophrenia patients, negative correlations emerged between negative symptoms and both robot’s and human’s negative face accuracy. Individuals do not respond similarly to human facial emotion and to non-anthropomorphic emotional signals. Humanoid robots have the potential to convey emotions to patients with schizophrenia, but their appearance seems of major importance for human-robot interactions.

The ability to follow one another’s gaze plays an important role in our social cognition; especially when we synchronously perform tasks together. We investigate how gaze cues can improve performance in a simple coordination task (i.e., the mirror game), whereby two players mirror each other’s hand motions. In this game, each player is either a leader or follower. To study the effect of gaze in a systematic manner, the leader’s role is played by a robotic avatar. We contrast two conditions, in which the avatar provides or not explicit gaze cues that indicate the next location of its hand. Specifically, we investigated (a) whether participants are able to exploit these gaze cues to improve their coordination, (b) how gaze cues affect action prediction and temporal coordination, and (c) whether introducing active gaze behavior for avatars makes them more realistic and human-like (from the user point of view). 43 subjects participated in 8 trials of the mirror game. Each subject performed the game in the two conditions (with and without gaze cues). In this within-subject study, the order of the conditions was randomized across participants, and subjective assessment of the avatar’s realism was assessed by administering a post-hoc questionnaire. When gaze cues were provided, a quantitative assessment of synchrony between participants and the avatar revealed a significant improvement in subject reaction-time (RT). This confirms our hypothesis that gaze cues improve the follower’s ability to predict the avatar’s action. An analysis of the pattern of frequency across the two players’ hand movements reveals that the gaze cues improve the overall temporal coordination across the two players. Finally, analysis of the subjective evaluations from the questionnaires reveals that, in the presence of gaze cues, participants found it not only more human-like/realistic, but also easier to interact with the avatar. This work confirms that people can exploit gaze cues to predict another person’s movements and to better coordinate their motions with their partners, even when the partner is a computer-animated avatar. Moreover, this study contributes further evidence that implementing biological features, here task-relevant gaze cues, enable the humanoid robotic avatar to appear more human-like, and thus increase the user’s sense of affiliation.

In this paper, we present the dynamical equations of a nonlinear adaptive natural oscillator (NANO) in order to exploit the natural dynamics in robotic systems. The presented oscillator tries to minimize an energy-based cost function by adapting the shape and frequency of the reference trajectory. Stability, convergence, and optimality of this oscillator are guaranteed analytically. Moreover, the performance of this oscillator is investigated by applying it to three different types of robotic models; i.e., the pendulum, the adaptive-toy, and the hopper-leg.

Gaze discrimination impairment in Schizophrenia severely affects social interactions and deteriorate patients’ quality of life. The AlterEgo develops therapeutic games using humanoids. To better understand these impairments we investigate in a systematic manner the effects that gaze has in dyadic joint action tasks. Specifically, we study the role that gaze cues play using the mirror game, a naturalistic scenario in which two players imitate each other’s hand motions. One of the two player is a humanoid robot, whose gaze can be controlled to give or not cues as to where it will move its hand next. In this talk, we report on a pilot study with heathy subjects. We measure the effect that the presence of these gaze cues have on the human subject’s performance at synchronizing her movement with that of the robot. Through post-hoc questionnaire, we also assess whether subjects perceive the robot as acting more human-like when producing gaze cue. A total of 43 subjects participated in the study. Results show that subjects are able to exploit the gaze cue in order to improve their performance. Moreover, participants found the robot not only more human-like, but also easier to interact with, in presence of gaze cue.

Many daily tasks involve spatio-temporal coordination between two agents. Study of such coordinated actions in human-human and human-robot interaction has received increased attention of late. In this work, we use the mirror paradigm to study coupling of hand motion in a leader-follower game. The main aim of this study is to model the motion of the follower, given a particular motion of the leader. We propose a mathematical model consistent with the internal model hypothesis and the delays in the sensorimotor system. A qualitative comparison of data collected in four human dyads shows that it is possible to successfully model the motion of the follower.

We present a data-driven method for designing parallel compliance. Designing such compliance helps the system to improve energy efficiency, mainly by reducing negative work. The core idea is to design a controller first and then find springs working in parallel with each actuator such that force-displacement graph is lined up around displacement axis. By doing so, we simply shape the natural dynamics for performing the task efficiently. Maximum torque reduction for actuators is a byproduct of this design method. The method can be used in different cyclic robotic application, especially in legged locomotion systems. In this paper, we design a spinal compliance for a bounding quadruped robot in Webots. The results show that the power consumption and the maximum torque are reduced significantly.

Having a direct impact on the energy efficiency has made the compliance a favorable element in the robotic systems. Moreover, legged system can benefit from compliance for stability, speed, adaptability and robustness. Recently, we have studied the effects of compliant spine in quadrupedal robots. We have observed that having nonlinearity in the spine compliance can set a better trade-off between speed and energy efficiency. Similar to the spine in quadruped robots, compliance at the hip joint of bipedal robots can also improve the walking performance such as robustness. Here, we test the efficacy of piecewise linear hip compliance for robust bipedal walking.

For robotic systems, energy efficiency is one the most crucial goals. Many studies have been done to accomplish this goal from design and control point of view. In the second view, one of the preferred method is to design the desired trajectory in harmony with the dynamics of the system; i.e. natural dynamics exploitation. Assuming a structure for the desired trajectory, such as sinusoidal trajectories, we can have a parameterized control system as in CPG-Network. Therefore, having an adaptation method for those parameters to reach energy efficiency can be beneficial to control of robotic systems.

We compare the effects of linear and piecewise linear compliant spines on locomotion performance of quadruped robots in terms of energy efficiency and locomotion speed through a set of simulations and experiments. We first present a simple locomotion system that behaviorally resembles a bounding quadruped with flexible spine. Then, we show that robots with linear compliant spines have higher locomotion speed and lower cost of transportation in comparison with those with rigid spine. However, in linear case, optimal speed and minimum cost of transportation are attained at very different spine compliance values. Moreover, it is verified that fast and energy efficient locomotion can be achieved together when the spine flexibility is piecewise linear. Furthermore, it is shown that the robot with piecewise linear spine is more robust against changes in the load it carries. Superiority of piecewise linear spines over linear and rigid ones is additionally confirmed by simulating a quadruped robot in Webots and experiments on a crawling two-parts robot with flexible connection.

We studied the effect of the control of an active spine versus a fixed spine, on a quadruped robot running in bound gait. Active spine supported actuation led to faster locomotion, with less foot sliding on the ground, and a higher stability to go straight forward. However, we did no observe an improvement of cost of transport of the spine-actuated, faster robot system compared to the rigid spine.

Within the field of quadruped robot research, much focus has been put on design of leg compliance and leg configuration [1, 2, 3, 4], and controller design [5]. Typically, design goals include robot speed, cost of transport, robustness against perturbations, and range of available speeds. Recently, research has started mimicking the spine of quadruped animals, both in the frontal and the sagittal plane. A widely accepted hypothesis predicts higher speed, resulting from active spine motion. Here we present results from hardware experiments with an active-spine equipped quadruped bounding robot, showing that through reduction of horizontal impulse the robot’s mechanical cost of transport was reduced.

The Basilisk Lizard’s striking ability to sustain highly dynamic legged locomotion on a range of surfaces from hard-ground to water is a remarkable feat [1]. Most legged robots would have diculty emulating this animal’s ability to robustly locomote on yielding or deforming surfaces. Therefore, to explore the dynamics of legged locomotion in this regime, we are studying the design of a bio-inspired water-running robot. Analyzing water-running dynamics may also help us gain insight into mobility on other yielding surfaces, such as granular media and mud.

Compliance became the essential part of locomotion in robotics. Due to ability of storing and releasing energy, compliance can be used for energy efficiency or reducing impact during ground collision and gaining robustness. On the other side, natural/passive dynamics are important because by exploiting such dynamics, energy efficiency will be assured. Therefore it is crucial to understand how compliance changes natural dynamics of a system. After this inspection, natural dynamics exploitation can be more straightforward through developing tools like adaptive oscillators. Such research to exploits natural dynamics of compliant system are reported in [1],[2] and [3]. Intuitively, it is known that using linear compliance will result in efficiency in only one mode. For instance, in mass-spring system for each spring constant, there is only one frequency where system is energy efficient. Using variable compliance is an attempt to overcome this problem and gain efficiency over a range of different setpoints or tasks. Great achievements reported using variable compliance in robotics application in [4] and [5]. Another way to overcome this problem is using nonlinearity. Natural dynamics and their multi-modality of efficiency will be discussed in this paper. It seems muscle-tendon units in biological systems are taking advantage of such nonlinearity in their compliance [6]. An adaptive oscillator based the one in [7] is presented in this work. This oscillator is able to exploit natural dynamics of system by shaping desired trajectory through frequency and phase lag.