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. 2019 Jun 3;16(1):65.
doi: 10.1186/s12984-019-0526-8.

Model-based control for exoskeletons with series elastic actuators evaluated on sit-to-stand movements

Jonas Vantilt  1   2 , Kevin Tanghe  3 , Maarten Afschrift  4   5 , Amber K B D Bruijnes  4 , Karen Junius  6 , Joost Geeroms  6 , Erwin Aertbeliën  3 , Friedl De Groote  4 , Dirk Lefeber  6 , Ilse Jonkers  4 , Joris De Schutter  3
Affiliations

Model-based control for exoskeletons with series elastic actuators evaluated on sit-to-stand movements

Jonas Vantilt et al. J Neuroeng Rehabil. .

Abstract

Background: Currently, control of exoskeletons in rehabilitation focuses on imposing desired trajectories to promote relearning of motions. Furthermore, assistance is often provided by imposing these desired trajectories using impedance controllers. However, lower-limb exoskeletons are also a promising solution for mobility problems of individuals in daily life. To develop an assistive exoskeleton which allows the user to be autonomous, i.e. in control of his motions, remains a challenge. This paper presents a model-based control method to tackle this challenge.

Methods: The model-based control method utilizes a dynamic model of the exoskeleton to compensate for its own dynamics. After this compensation of the exoskeleton dynamics, the exoskeleton can provide a desired assistance to the user. While dynamic models of exoskeletons used in the literature focus on gravity compensation only, the need for modelling and monitoring of the ground contact impedes their widespread use. The control strategy proposed here relies on modelling of the full exoskeleton dynamics and of the contacts with the environment. A modelling strategy and general control scheme are introduced.

Results: Validation of the control method on 15 non-disabled adults performing sit-to-stand motions shows that muscle effort and joint torques are similar in the conditions with dynamically compensated exoskeleton and without exoskeleton. The condition with exoskeleton in which the compensating controller was not active showed a significant increase in human joint torques and muscle effort at the knee and hip. Motor saturation occurred during the assisted condition, which limited the assistance the exoskeleton could deliver.

Conclusions: This work presents the modelling steps and controller design to compensate the exoskeleton dynamics. The validation seems to indicate that the presented model-based controller is able to compensate the exoskeleton.

Keywords: Assistive robots; Exoskeleton; Model-based control; Muscle weakness; Paraplegia; Series elastic actuator; Sit-to-stand.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Fig. 1
Fig. 1
General control scheme for an exoskeleton. The physical system in red is separated from the control by the dashed line. The control is divided into four hierarchical levels, with a few keywords to indicate their function. The thin lines represent data flow from the available exoskeleton sensors. The thick lines represent the control/decision commands to a lower control level. The assistance block in green transforms the sensor data to desired assistance in the low-level control block
Fig. 2
Fig. 2
Floating base model of the exoskeleton. The floating base representation of an exoskeleton is characterized by a virtual, unactuated chain. This chain consists of six dofs: three translations and three rotations in 3D. When using a 2D model this reduces to two translations and one rotation, shown by the filled dofs. These actuators lie in one plane, the sagittal plane, shown in blue
Fig. 3
Fig. 3
Schematic model of an SEA. An SEA consists of a motor, a transmission, a spring and the outgoing link, as shown by the top schematic. All variables are referenced against the previous link as shown by the dashed line in the lower figure. θi∗ is the motor angle before transmission. αi=θi−ϕi is the spring deflection angle
Fig. 4
Fig. 4
Definition of frames, angles and floating base states variables of the exoskeleton. The thick black lines represent the link of one leg of the exoskeleton viewed from the side (sagittal plane). The joints (hip, knee and ankle are indicated by black circles. The lever arms of the actuated joints are indicated by purple bars. The frame of each link is shown in a different color with all z-axes pointing outward of the paper. The link angles ϕi and the lever arm angles θi are defined starting from the previous link (=reference link) and according to the right hand rule. The knee joint and lever arm angle are thus negative in this configuration. px and py represent the position of the center of mass of the floating base link, the pelvis link. The angle ψ is the angle of the floating base with respect to the world frame
Fig. 5
Fig. 5
The MIRAD sit-to-stand exoskeleton. A side view of the MIRAD sit-to-stand exoskeleton is shown. The power and communication cables for each joint are not present to avoid overload of the photograph. The MACCEPA actuators are placed at the hip, knee and ankle of a commercial lower limb brace
Fig. 6
Fig. 6
The MACCEPA actuator. The motor is connected to the lever arm with a toothed belt transmission. A flat cable connects the lever arm with the compression spring located in the moving output link. When the lever arm and output link are aligned, the torque generated by the MACCEPA is zero. The pretension screws allow to give the spring a pretension to change the stiffness relationship of the actuator
Fig. 7
Fig. 7
Different contact situation of the sit-to-stand motion. In the sit-to-stand motion, seat-off is the key event for modelling. In the sit state, the exoskeleton is supported by the stool and only the inertial, centrifugal and Coriolis terms are compensated for (only the trunk can move). In the stand state, the exoskeleton is no longer supported by the stool and needs to support its own gravity
Fig. 8
Fig. 8
Mid-level controller of the exoskeleton. The Finite State Machine of the sit-to-stand motion has four main states: sit, stand, standing-up and sitting-down. Four events trigger the change from state to state. In the sit state only the inertial and Coriolis compensation of the exoskeleton is active. In the standing-up state, the gravity compensation is gradually turned on before the seat-off. When the compensation gets one or when the seat-off is detected, the gravity compensation is completely on. When the event to start the assistance is detected, the assistance is switched to active. In the stand state the exoskeleton is completely compensated. In the sitting-down state, gravity compensation is gradually reduced to zero until the person sits back on the stool
Fig. 9
Fig. 9
Overview of the exoskeleton controllers. The control loops of the exoskeleton are given. The actuator controller is a velocity controller of the motor angle θ. The input of this actuator controller comes from the low-level controller: the desired velocity and the velocity feedforward. Both signals use the dynamic model and the model of the spring. The feedforward θ˙ff is obtained from Eq. (13-14)
Fig. 10
Fig. 10
Comparison of muscle effort in three conditions: passive, transparent and without exoskeleton. The average muscle effort (time integral of the muscle activity) is shown relative to the transparent condition by the gray bars and the corresponding standard deviation across all fifteen participants is shown by the error bars. Each muscle is scaled separately relative to the corresponding average muscle effort in the transparent condition. The black dotted line represents this relative muscle activity in the transparent condition, scaled to one. In the left subfigure (a) the muscle effort of the passive condition is compared to the transparent condition. In the right subfigure (b) the effort of the condition without exoskeleton is compared to the transparent condition. When the plotted bars and error bars lie above one, the muscle effort is larger than in the transparent condition. Significant differences between the without exoskeleton and transparent condition are marked with a black star (pBonferroni−Holm<0.05)
Fig. 11
Fig. 11
Comparison of human joint kinematics and dynamics in three conditions: passive, transparent and without exoskeleton. The human kinematics and joint torques of the hip, knee and ankle are shown in three conditions: without exoskeleton (N) in green, the transparent exoskeleton condition (T) in red and the passive exoskeleton condition (P) in black. The top three subfigures (a to c) represent the joint angles, while the lower three subfigures (d to f) represent the joint torques, normalized with respect to the mass of each participant. Both the average and standard deviation (band of ±σ are shown in each graph. The blue bars indicate time periods with a significant difference between the passive and transparent condition of the post-hoc two-sample t-test. The corrected p-values are 0.008, <0.001, 0.007 and <0.001 for the hip angle, knee angle, hip torque and knee torque respectively
Fig. 12
Fig. 12
Exoskeleton transparent control evaluation. The joint torque analysis for the transparent condition is shown (condition T). The top three subfigures (a to c) show the joint torque for the hip, knee and ankle for one STS motion. The desired joint torque τdes,spr is shown in blue. This desired spring torque is torque needed to compensate the exoskeleton. The measured spring torque τ^spr is represented in red. The torque to accelerate the motor inertia is given in yellow. Seat-off occurs at the black dashed line. The lower three subfigures (d to f) show the average error (difference) and the band of standard deviation (±σ) between the desired τdes,spr and the delivered τ^spr spring torques for all the STS motions of condition T
Fig. 13
Fig. 13
Exoskeleton joint torque control evaluation. The joint torque analysis for the offline assistance-as-needed is shown (condition A). The top three subfigures (a to c) show the joint torque for the hip, knee and ankle for one STS motion. The desired joint torque τdes,spr is shown in blue. This desired spring torque is the sum of the exoskeleton dynamics compensation torque τdyn, shown by the light blue curve, and the desired assistance indicated by the blue area between τdyn and τdes,spr. The realised spring torque τ^spr is represented in red. The torque to accelerate the motor inertia is given in yellow. Seat-off occurs at the black dashed line. The lower three subfigures (d to f) show the average error (difference) and the band of standard deviation (±σ) between the desired and the delivered spring torques for all the STS motions of condition A
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