## 1 Introduction  
Mobility aids reduce the fall risk, increase the autonomy, and improve the quality of life of persons with walking difficulties. Wheeled walkers, known as rollators, are widely used to assist in mobility. In the past decade, robotic walkers have gradually been developed and have attracted the interest of many researchers [1; 2; 3]. Different from the traditional rollator, the sensors embedded in robotic walkers collect information on the gait, and the in-wheel motors provide assistance during walking. When the user pushes the handle of the robotic walker to operate it, the user's intention becomes significant [4; 5]. For instance, the weighted-frequency Fourier linear combiner-Fourier linear combiner algorithm was proposed to extract the voluntary user's command in the walker-assisted gait [6]. A robotic walker was proposed for the adjustment of the motion direction and velocity of the user based on signals from infrared sensors [7]. In addition to the user's intention during assisted walking, the gait alternation with or without conventional rollators has also been investigated. In [8], the authors investigated the biomechanical effects of a rollator on the walking patterns of healthy subjects (age: 35\(\sim\)74 years). Their results showed increased hip flexion, reduced ankle dorsiflexion and knee flexion, and reduced ankle and, especially, knee joint moments. The use of a rollator was found to increase the walking speed of elderly subjects(mean age: 82 years) [9] and significantly reduce the lower-limb muscle activity of healthy subjects (age: 22\(\sim\)70 years) [10]. A conventional rollator can be considered as a payload to push as it sustains the weight of the user during walking. Human-machine interactions affect the movements of the user and walker during walker-assisted walking. For robotic walkers, the external force is provided by the motors, and its movements can be much more complex than those of a conventional rollator. The gait dynamics of the user might consequently be affected by the movement of the robotic walker. Therefore, the application of robotic walkers could result in issues regarding changes in gait, different from those related to rollator-assisted walking. However, to the best of our knowledge, few studies have been conducted on the gait analysis during robotic walker-assisted walking. An overall reduction in the spatio-temporal parameters, especially the gait speed, was observed during robotic walker-assisted walking [11]. For the development and recommended daily use of robotic walkers, this topic must thoroughly investigated, as also mentioned in [11]. Conventional approaches to reduce the spatio-temporal parameters, such as the analysis of the gait parameters and kinematics, only examine the nature of the gait patterns instead of the inherent dynamical nature of locomotion. For the walking movement, nonlinear time series analysis offers a way to measure the dynamic properties of gait, such as local dynamic stability (or periodicity), complexity, and determinism. The local dynamic stability is usually expressed by the maximum Lyapunov exponent [12] and maximum Floquet multipliers [13; 14], while the gait complexity can be evaluated by multiscale entropy [15] and permutation entropy [16]. The determinism of a time series indicates whether the time series contains a deterministic component or is purely stochastic. A technique was introduced to distinguish between deterministic chaotic and truly random behaviors [17]. The percentage of determinism (%DET) is a measure use in recurrence quantification analysis (RQA) and is related to the predictability of dynamical systems; a large %DET value indicates the presence of deterministic patterns in the dynamics of the time series. Investigations of gait data based on nonlinear time series with or without a robotic walker enable the deduction of useful information regarding the intrinsic dynamical changes.