Adjustment of instantaneous reference walking speed during synchronized robot-based gait rehabilitation

1 Introduction

During the last two decades, several robotic devices have been developed to improve the gait rehabilitation process [1], including treadmill-based systems and mobile devices for over-ground training, among other types. Robotic systems that possess a compliant behaviour (e.g. when using impedance control strategies) allow the patients to deviate from the reference trajectories initially set for the therapy, which may cause synchronization problems between the reference and the actual (patient’s) trajectories. To tackle these problems, different synchronization methods have been presented, which include trajectory adaptation algorithms based on the interaction forces between the device and the patient [2], cyclic [3] and continuous [4] adjustments of the trajectory generator replay speed, and the implementation of adaptive oscillators to adjust the temporal [5] or spatio-temporal parameters [6] of the reference gait patterns, or to adapt the support torque exerted by the system to assist the patient [7].

Many of these synchronization methods are applied in systems that use a treadmill or a mobile platform. However, it is often not specified how the synchronization efforts affect the reference inputs of the controllers that regulate the instant speed of the treadmill or mobile frame. If the online adjustments of the trajectory generation’s temporal parameters fluctuate significantly throughout the gait cycle, applying them directly to the inputs of the velocity controllers may cause an undesired oscillatory behaviour.

This paper presents a method to adjust the inputs of the velocity controllers of the mobile platform of the MOPASS system [8] (Figure 1), a robotic device for over-ground gait rehabilitation with active hip and knee joints for motion assistance in the sagittal plane. The presented method was tested with different simulation scenarios and with a healthy subject using MOPASS, running a synchronization algorithm based on the concept presented by Aoyagi et al. in [4]

2 Synchronization method

In order to provide the reference trajectories for the system, MOPASS possesses a trajectory generator which creates hip and knee motion profiles depending on its input and on the reference cadence set by the therapist. The input of the generator in an instant k is

where Δt = 1/f_c is the time elapsed between two consecutive samples, f_c is the sampling frequency of the generator and Δt_comp corresponds to a time compensation element (i.e. the synchronization effort).

Figure 1

MOPASS system.

The value of Δt_comp is obtained by means of a phase controller working together with a phase estimator (based on [4]). The latter is in charge of comparing the reference gait pattern to the state of the actual gait trajectories, in order to estimate the current phase (i.e. the normalized time or percentage of the stride period) of the patient’s gait. The estimated phase t_n* = [0%, 100%) is obtained by finding the t_i that minimizes the cost function

where N = 4 is the number of joints, θ_{j, act} is the actual position of joint j, θ_{j, ref}(t_i) is the reference position of joint j at a given normalized time (phase) t_i = [0%, 100%), h_{p, act} and d_{p, act} are the actual vertical and horizontal positions of the foot from the leg p = {L:left, R:right} with respect to the hip joint calculated from the actual joint angles, h_{p, ref}(t_i) and d_{p, ref}(t_i) are the vertical and horizontal positions of the foot of leg p calculated from the reference joint angles at a given normalized time t_i, t_n = [0%, 100%) is the normalized time value corresponding to the current input of the generator, t_n*[k − 1] is the estimated normalized time (phase) from the previous iteration, and W is the vector of weights. The normalization of the time is done straightforwardly:

where mod is the modulo operation and T_ref is the reference gait cycle period (i.e. the stride period).

With the estimated value t_n*, it is possible to calculate the phase error between the actual and the reference gait patterns. This error is fed to a PI phase controller component in charge of yielding the time compensation velocity υ_t-comp, which is finally used to compute the time compensation Δt_comp. A simplified diagram of the synchronization process is shown in Figure 2.

Figure 2

Scheme of the synchronization method.

Figure 3

Initial adjustment of the platform speed.

3 Mobile platform speed

The mobile platform of the MOPASS system is controlled by two drives located in the two motorized wheels. Disregarding the synchronization effort, the inputs to the (angular) velocity controllers in the drives is given by

where FD_ref is the total horizontal displacement with respect to the hip joint of the foot along the sagittal axis in a cycle (using the reference trajectories), K_SL =0.85 is a proportional multiplier and r is the radius of the wheels.

Initially, the time compensation was applied directly to the adjustment of the platform speed using a simple low-pass filter to reduce the oscillations in the speed (Figure 3). However, this solution generated an undesired oscillatory behaviour in the platform speed. To reduce these oscillations, a second approach was taken, (Figure 4), which included some new components. First, a gait phases’ detector that identifies the moment of initial contact of the main leg (i.e. the one that performed the first step) and, therefore, its swing to stand transition. The second component is a cyclic average filter, which computes the average of the reference platform speed (and updates its output) every time an initial contact is detected. This average value is finally fed to the low-pass filters to smoothen the velocity input of the controllers.

Figure 4

Final adjustment of the platform speed.

Figure 5

Simulation results. Blue: initial method. Red: improved method.

Figure 6

Test results with a healthy subject using MOPASS.

4 Tests and results

Initially, the platform-speed adjustment method was assessed in three different simulated scenarios. For the simulations, two different sets of trajectories were used: one was set as the reference gait pattern and the other one as the (simulated) actual one. In scenario A, both gait patterns had the same gait cycle period (T_act = T_ref); in scenario B, T_act = 0.85 ⋅ T_ref; and in scenario C, T_act = 1.15 avoid T_ref. The simulation results are shown in Figure 5, where the resulting instantaneous platform speeds corresponding to the initial and the improved methods are depicted, together with the corresponding estimated phase error. It can be seen how the inclusion of the cyclic average filter reduced significantly the oscillations in the walking speed, although the system needs more time to react to the phase controller compensations.

A second assessment of the methods was done with a healthy subject performing over-ground walking with the MOPASS system. The subject was asked to walk slowly, then to increase significantly the speed, and finally to reduce the speed and walk slowly again. The test results can be seen in Figure 6, where the platform speed is shown, together with the reference and actual joint trajectories. As with the simulations, a reduction on the oscillatory behaviour of the platform speed can be seen when using the cyclic filter. Moreover, the subject informed that the initial method yielded uncomfortable changes of the speed, whereas the improved method had a much more smooth behaviour during the exercise without feeling a lagged reaction of the platform to the speed changes.

5 Conclusion

This paper presented a method to adjust the instantaneous speed used as reference by robotic gait rehabilitation systems (e.g. the speed of the treadmill or mobile frame) during compliant, synchronized therapy. This method is particularly useful when the synchronization algorithms generate compensations that fluctuate significantly throughout the gait cycle. The speed adjustment method was tested with a synchronization method composed by a phase estimator and a phase controller than generates continues temporal-compensations. After carrying out simulations and initial tests with a healthy subject using a mobile rehabilitation device, a reduction of the oscillatory behaviour of the speed was seen, yielding smoother speed profiles that felt more comfortable to the test subject.