Flexible Assistance using Adaptive Oscillators: Model-based and Model-free Approaches Renaud Ronsse, Nicola Vitiello, Tommaso Lenzi, Stefano M. M. De Rossi, Bram Koopman, Edwin H. F. van Asseldonk, Jesse van den Kieboom, Herman van der Kooij, Maria Chiara Carrozza, and Auke Jan Ijspeert Fig. 1. Sketch of the synchronization between the human joint (elbow in this case) and an adaptive oscillator. Recent findings in rehabilitation robotics suggest that therapies are more successful if the patient actively par- ticipates to perform the intended movement, giving rise to the concept of “assist-as-needed” [1], [2]. However, to date, the commercial solutions for lower limb rehabilitation still rely on older paradigms based on the stiff control of a reference trajectory specified by the experimenter [3]. With this approach, the patient will be maximally supported by the robot, regardless of his own contribution or capabilities. Moreover, the reference trajectory is based on recordings from healthy persons, and may not be entirely suitable for the patient being trained. Consequently, independent clinical studies hardly managed to illustrate any advantage of robot- based therapies over classical therapies, so far [4], [5]. In the present contribution, we propose a new approach to provide assistance-as-needed during cyclical movements. This approach is based on adaptive oscillators, that were developed by Righetti et al. [6] for various applications [7]. Oscillator-based methods are appealing in the context of rhythmic movement assistance, because these movements — like e.g. walking — are likely controlled by spinal oscillators [8]. The “artificial” oscillator is thus assumed to synchronize with the spinal one, and in turn feeds back some torque to the assisted joint (Figure 1). Note that synchronization is This work was supported by the EU within the EVRYON Collaborative Project STREP (FP7-ICT-2007-3-231451). R. Ronsse, J. van den Kieboom, and A.J. Ijspeert are with the Biorobotics Laboratory, Institute of Bioengineering, ´ Ecole Polytechnique F´ ed´ erale de Lausanne, CH-1015 Lausanne, Switzerland. e-mail: {renaud.ronsse,jesse.vandenkieboom, auke.ijspeert}@epfl.ch N. Vitiello, T. Lenzi, S.M.M. De Rossi, and M.C. Carrozza are with the ARTS lab, Scuola Superiore Sant’Anna, I-56025 Pontedera (Pisa), Italy. e-mail: {n.vitiello,t.lenzi,s.derossi,carrozza} @sssup.it B. Koopman, E.H.F. van Asseldonk, and H. van der Kooij are with the Laboratory Biomechanical Engineering, University of Twente, NL-7500 AE Enschede, the Netherlands. e-mail: {b.koopman,e.h.f.vanAsseldonk,h.vanderKooij} @ctw.utwente.nl ubiquitous in biological systems [9], like in multi-persons coordination dynamics [10]. In our new approach, we spec- ulate that the adaptive oscillator will synchronize with the user’s movement in a similar way as the therapist would do when assisting the patients during exercise. Our contribution will particularly focus on two experi- ments we conducted over the last year. The first experiment was designed as a proof of concept [11]. We focused on (quasi-)sinusoidal movements about the elbow joint (as pictured in Figure 1), in order to avoid dealing with complex dynamics due to multi-joints coordinations and interactions with the ground. The artificial oscillator was based on an augmented Hopf oscillator [6]. From a (quasi-)sinusoidal input θ (t ), this dynamical system is able to extract the instan- taneous movement features, namely frequency ω , amplitude A, and offset C, while keeping its output phase φ synchro- nized with the input. Therefore, a smoothed but synchronized estimate of the input can be obtained — ˆ θ = A sin φ + C — as well as estimates of the higher order derivatives: velocity: ˆ ˙ θ = Aω cos φ , and acceleration: ˆ ¨ θ = −Aω 2 sin φ . The main advantage of this approach with respect to classical filtering is that neither ˆ θ , nor ˆ ˙ θ and ˆ ¨ θ are delayed with respect to the actual position, velocity, and acceleration. This is because the oscillator exploits the a priori knowledge that the movement is periodic. Using the estimates of position, velocity, and acceleration, an estimate of the applied torque can be obtained using an inverse dynamical model: ˆ τ = f ( ˆ θ , ˆ ˙ θ , ˆ ¨ θ ). Finally, a fraction of this torque can be fed back to the user, using an assistive device. This approach was successfully applied to healthy individuals using an elbow exoskeleton [12]. Figure 2 shows the biceps and triceps EMG measured on a representative participant during cyclical flexion-extension of the elbow of constant amplitude and frequency. The figure reveals that a significant decrease of the participant effort was obtained by switching the assistance on (black dots), while this decrease was instantaneously washed out once assistance was removed (dark gray dots). Because of the oscillator intrinsic adaptivity, this approach left the user free to change the movement amplitude and frequency, as demonstrated by complementary data. A second experiment is currently performed to translate this approach for a more functional task, namely walking. For this aim, we use the LOPES, a lower-limb exoskeleton robot for interactive gait rehabilitation [13]. The dynamics of walking introduce two extra challenges with respect to