Velocity-dependent reference trajectory generation for the LOPES gait training robot

2011 IEEE International Conference on Rehabilitation Robotics Rehab Week Zurich, ETH Zurich Science City, Switzerland, June 29 - July 1, 2011 Velocity-dependent reference trajectory generation for the LOPES gait training robot N. Tufekciler, E.H.F. van Asseldonk, H. van der Kooij Department of Biomechanical Engineering MIRA, University of Twente Enschede, The Netherlands a.n.tufekciler @utwente.nl H. van der Kooij Dept. of Biomechanical Engineering Delft University of Technology Delft, The Netherlands Abstract The aim of this study is to assess the feasibility of an approach for generating velocity-dependent trajectories to train neurologically injured patients. The reference trajectories are constructed based on the gait patterns of subjects walking on a treadmill. By extracting key events (parameters) from these trajectories, the velocity dependency of the parameters is determined by regression analysis. Then, splines are fitted through these points to obtain gait patterns (position, velocity and acceleration) for specific walking velocities. Considering the severely injured patients, a feedforward controller is used in addition to the impedance controller. The approach is implemented on the LOPES gait rehabilitation robot and evaluated on healthy subjects. Results indicate that the subjects can walk naturally in the robot with the constructed reference trajectories. Further improvements to the technical design and additional testing of healthy and impaired subjects are required to show whether this approach can be transferred to clinical domain. Index Terms Exoskeletons, gait therapy, rehabilitation robots, gait, neurorehabilitation. I. INTRODUCTION Major developments have been taking place in the field of rehabilitation of locomotion in stroke and spinal cord injured individuals during the last decades. Treadmill training is one of the important rehabilitation techniques. In manually assisted treadmill training, the patients stand on a treadmill and repetitive functional movements are generated to improve gait and lower limb motor function in patients with locomotor disorders [1] [3]. The walking-like leg movements are generated and or assisted by manual handwork of two physiotherapists. Since this kind of training is in general physically demanding for the therapists, treadmill training has been automated to increase the duration of the training and to reduce the effort of the physiotherapists. Therefore, several robotic devices have been developed to overcome these deficiencies. The first generation of these devices has been in clinical use for several years: the Lokomat [4], the AutoAmbulator [5] and the Gait Trainer [6]. To control these devices, it is essential to define a reference trajectory. The most common way of determining the prescribed gait pattern is modeling the trajectory based on norma- This study was supported by a VENI grant (grant nr: 91610143) from The Netherlands Organisation for Scientific Research and by a grant from the Ministry of Economic Affairs and province of Overijssel, the Netherlands (grant: PID 082004). tive movements such as defining pre-recorded trajectories from unimpaired volunteers [7] or pre-recorded trajectories during therapist guided assistance. Some other strategies include generating a trajectory for the paretic leg by using the actual motion of the non-paretic leg [8] and scaling the trajectory parameters for producing different gait patterns [9]. Determining the desired trajectory for the robotic controller is one of the challenges that must be specified. Studies have shown that to determine the reference trajectories for gait training, walking velocity must be considered for its influence on the shape of the gait pattern [10]. Kirtley et al. [11] shows the influence of velocity on knee flexion angle and the duration of the stance phase. Lelas et al. [12] and Stoquart et al. [13] derive regression equations for hip and knee kinematic parameters and demonstrate the dependency of the relative timing of peak sagittal plane parameters to velocity. The relative stance phase duration and double support time also depends on velocity. In this study, the velocity-dependent reference trajectories are developed and implemented into the compliant gait trainer robot LOPES [14]. The presented approach imposes a complete gait pattern based on the analysis of the gait patterns of subjects walking on a treadmill. The goal of this study is to show the feasibility of the control strategy based on velocitydependent reference trajectories for the whole gait cycle. A. Subjects II. METHODS Three healthy young adults (2 male, 1 female; aged 24-26, weight 60-80 kg, height 1.70-1.80 m) volunteered for the experiment. All subjects gave written informed consent to participate in this study. B. Experimental apparatus and recordings For the experiment the prototype of the gait rehabilitation robot LOPES was used. LOPES is an exoskeleton-type rehabilitation robot with 8 actuated degrees of freedom: pelvic horizontal translations and hip abduction/adduction, hip flexion/extension and knee flexion/extension of both legs. It is lightweight and actuated by Bowden-cable-driven series elastic actuators [15]. The robot is impedance controlled, which implies that the actuators are used as force (torque) sources. 978-1-4244-9861-1/11/$26.00 2011 IEEE 567

The torque for each joint is controlled and has a torque control bandwidth of 16 Hz. C. Determination of reference trajectories The reference trajectories were constructed for the hip abduction/adduction, hip flexion/extension and knee flexion/extension joint angles. The reference gait patterns were based on measurements of 12 healthy subjects walking on treadmill at seven different velocities: 0.5 km/h, 1 km/h, 2 km/h, 3 km/h, 4 km/h, 5 km/h, 6 km/h. The gait parameter recordings were performed using an optical tracking system (Vicon Oxford Metrics, Oxford, UK). Passive reflective markers were placed on both sides of the subjects bodies. All markers were recorded at a sampling rate of 120 Hz. Motion data was converted to joint and segment kinematics using custom-written software [16]. The 3D joint angles of ankle, knee, hip and the 3D centre of mass (CoM) of the pelvis segment were analyzed. The calculated lower limb joint angles were split into steps and these steps were parameterized by defining a number of points on each step at key characteristic points such as the peak values in position and velocity data, starting and ending of each trajectory, and some other extra parameters with fixed timing points to reduce fitting errors, as illustrated in Figure 1. Every point had a timing, and a position,velocity and acceleration amplitude. The median value of each parameter for each subject was computed for the given joint angles at each walking speed. Fig. 1. Locations of the parameterization points of the hip abduction, hip flexion and knee flexion joint angle trajectories. Then, a mathematical relation between velocity and the individual parameter values was determined with regression analysis. The contribution of leg length, walking velocity and walking velocity square was determined by stepwise regression to predict the value of that specific parameter. Finally, to construct the reference trajectories for the desired velocities, the parameter values were determined using the derived regression equations. Then, splines were fitted through the regressed parameters. Since it was desired to obtain the joint trajectories with angular positions, velocities and accelerations, sixth order splines in B-form were specified. The velocity and acceleration references were calculated by taking the first and second analytical derivatives of the fitted splines, respectively. The Figure 2 illustrates the complete construction process. Fig. 2. D. Controller Overview of the velocity-dependent reference trajectory generation. In this study, the implemented control strategy consisted of Feedforward and Feedback components. The Feedforward component was used to predict torques required to follow the desired trajectory given by the desired joint angles, velocities and accelerations. An identified inverse dynamic model of the robot defined by a double pendulum model with a two-segment swing leg was used to calculate the Feedforward component τ ff = M(q) q + C(q, q) q + G(q), (1) where q, q, q denotes joint angles, angular velocities and angular accelerations and M(q) q, C(q, q) q, and G(q) specify the inertial, coriolis and gravitational moments of the robot, respectively. The velocity-dependent reference joint angles q were obtained as described in Section II-C. The controller was applied in the sagittal plane. In the lateral plane, only the gravity component of the robot was compensated. The feedback component was used to ensure that the virtual impedance allowed a variable deviation from the desired trajectory. The actual joint positions were virtually coupled to the reference positions by a simulated spring and damper system with spring stiffness K p and damping constant K v. The feedback controller was calculated by τ fb = K p e + K v ė, (2) with e = q ref q and K p = 300 Nm/rad gain for maximum stiffness which was chosen considering compliance and stability purposes. For the combination of predefined joint trajectories and impedance control an inappropriate timing could result in unwanted and uncomfortable interactive forces when the subject and robot walked too much out of phase. To prevent this situation from occurring, an algorithm introduced by Aoyogi et al. [17] was used. The algorithm synchronized the reference trajectories in real-time to the actual motion of the individual. E. Protocol Subjects walked in the LOPES under three different conditions: 1) Zero Impedance control: three trials were run with 1 km/h, 2 km/h and 3 km/h walking velocity, 2) Feedforward control: three trials were run with 1 km/h, 2 km/h and 3 km/h walking velocity, 3) Impedance with Feedforward control: three trials were run with 1 km/h, 2 km/h and 3 km/h walking velocity. Impedance controller was set to its maximum stiffness. At start, subjects walked for five minutes in Zero Impedance to get acquainted with the robot. The order of the conditions was randomized. Under each condition, the 568

Fig. 3. Comparison of the reference trajectories (solid line) with the average measured trajectories (dashed line) from treadmill walking at walking speeds of 1 km/h (red line), 2 km/h (green line), and 3 km/h (blue line). angular positions and moments from hip and knee joints were recorded. Prior to the trials, subjects were instructed to walk as normal and consistently as possible. F. Data Analysis The steps were normalized such that each consists of 100 samples. The steps were grouped according to the experiment and walking velocities, and then steps of the last 30 seconds were averaged to create a mean step for each condition. III. RESULTS A. Constructed Reference Trajectories The reference trajectories were constructed through the parameters that were determined by the equations obtained from the regression analysis. To verify the accuracy of the approach, Figure 3 compares the constructed position, velocity, and acceleration trajectories with the average measured trajectories of treadmill walking for hip abduction, hip flexion and knee flexion joints at walking velocities 1 km/h, 2 km/h and 3 km/h. The velocity and acceleration references were calculated by taking the analytical first and second derivatives of the reference positions, respectively. In general, the results showed that the deviations were within an acceptable range of motion. However, a relatively larger deviation from the measured trajectory could be observed at the hip abduction joint indicating that the chosen spline characteristics were not well-suited to fit the data. Additionally, a relatively larger deviation at the hip flexion joint before heelstrike and at the knee flexion joint during stance for slower velocities could indicate improper placement of the parametrization points which could be related to the regression method. B. Evaluation of The Reference Trajectories To compare the reference trajectories with respect to the subjects gait patterns, the mean walking trajectories under different controllers were plotted with the reference trajectories for three different velocities as shown in Figure 4. The walking patterns of subjects in Zero-Impedance control was relatively different from the reference trajectories. In Zero- Impedance, the dynamics of the robot was not compensated and this could explain the difference between treadmill walking and walking in LOPES. The Feedforward control approach was implemented to compensate the robot dynamics and the differences between treadmill walking and walking with the robot. Results demonstrated that the measured hip flexion and knee flexion joint trajectories in Feedforward control differed less from the reference trajectories with respect to Zero-Impedance with a greater hip and knee extension. As the walking velocity increased, the subjects measured trajectories drew closer to the references. According to the subjective feedback, the subjects also experienced more comfort while walking under Feedforward control. An additional evaluation was conducted by applying a Feedback controller with the Feedforward controller, concerning the suitability of the references to the impaired subjects. The reference patterns were tracked smoothly under maximum stiffness, which confirmed that the approach could also ensure a normal walking pattern for the patients. 569

Zero Impedance Feedforward Impedance with Feedforward Fig. 4. Mean hip (red solid line) and knee (blue solid line) joint trajectories of the last 30 seconds of each controller at each walking speed, compared to the reference trajectories (dashed lines). IV. DISCUSSION In this study, a method for constructing the velocity dependent reference trajectories was presented. The appropriatness of these trajectories was evaluated with an experiment in which the measured trajectories showed minor deviatons from the reference trajectories with the application of the Feedforward controller. As the constructed trajectories were compared with the mean healthy subject data walking on treadmill, small deviations could be observed. The number of regressed parameters for constructing the splines can be increased to improve the fitting accuracy of the trajectories. Additionally, the spline characteristics can be adjusted for local control over the splines. A simple inverse dynamic model of the robot for the sagittal plane motion was used that could have limited the performance of the controller. The model can be extended with additional properties by considering the hip abduction movement. The Feedforward torque can improve walking in LOPES by compensating the inertia of the robot additionally in lateral direction. The inverse model can also be used to compensate the inertia of the human limbs during swing phase by feeding the appropriate human limb parameters to the model. V. CONCLUSION For the treatment of severely impaired patients, the feasibility of the control approach to apply support for whole gait cycle was demonstrated. For constructing the reference trajectories, use of splines allowed accurate modeling of natural gait patterns at various velocities. Experiments showed that healthy subjects can walk in the robot with reasonable comfort and natural gait pattern. The positive influence of the velocity-dependent reference trajectories on subjects motivates further investigation. Future improvements will aim at clinical evaluations of the proposed approach. ACKNOWLEDGMENT The authors would like to thank subjects who participated in the study, and B. Koopman, who fundamentally contributed to the experiments. REFERENCES [1] H. Barbeu, M. Ladouceur, K. E. Norman, A. Pepin, and A. Leroux, Walking after spinal cord injury: Evaluation, treatment, and functional recovery, Arch. Phys. Med. Rehabil., vol.80, no.2, pp. 225-235, 1999. [2] V. Dietz, G. Colombo, and L. Jensen, and L. Baumgartner, Locomotor capacity of spinal cord in paraplegic patients, Ann. Neurol., vol. 37, pp. 574-582, 1995. [3] V. Dietz, G. Colombo, and L. Jensen, Locomotor activity in spinal man, Lancet, vol. 344, pp. 1260-1263, 1994. [4] R. Riener, L. Lnenburger, I. Maier, G. Colombo and V. Dietz, Locomotor training in subjects with sensori-motor deficits: an overview of the robotic gait orthosis Lokomat. Journal of Healthcare Engineering, vol. 1, no. 2, pp. 197-216, 2010. [5] S. Hesse, D. Uhlenbrock, and T. Sarkodie-Gyan, Gait pattern of severely disabled hemiparetic subjects on a new controlled gait trainer as compared to assisted treadmill walking with partial body weight support, Clin. Rehabil., vol. 13, pp. 401-410, 1999. [6] D. Uhlenbrock, S. Hesse, A mechanized gait trainer for restoration of gait, Journal of Rehabilitation Research and Development, vol. 37, pp. 701-708, 2000. [7] R. Riener, L. Lunenburger, S. Jezernik, J.M. Anderschitz, G. Colombo, and V. Dietz, Patient-cooperative strategies for robot-aided treadmill training: first experimental results, Neural Systems and Rehabilitation Engineering, IEEE Transactions on, vol. 13, no. 3, pp. 380-394, 2005. 570

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