## 4 Discussion
### Methods Applied to the Currently Available Exoskeleton Robots  
In robotic rehabilitation, exoskeletons have been developed to assist patients after stroke by moving their impaired limb through a predefined trajectory. Trajectory generation is a fundamental topic in the design of these robots because of the growing number of stroke patients. The usual approach with most exoskeletons is to use a prerecorded trajectory as a look-up table. There are some limitations to this method, including data storage limitations and poor tuning relating to the motion's parameters. According to the classification in Section 3, two motion planning approaches are used for current upper limb exoskeletons: the traditional approaches based on Cartesian motion planning and inverse kinematics and approaches based on learning by demonstration (LbD). In the first approach (Table 1), cubic and polynomial methods are the most used in current exoskeletons. The limitation of these methods is that they require the calculation of too many parameters (polynomial coefficients), and the generated trajectories are un-natural. An alternative is the optimization-based methods: (i) based on optimization of a cost function such as minimum-jerk, minimum-torque-change, and inertia-like models; (ii) based on the extraction of principal motion patterns like principal component analysis (PCA) (as in [45]) and functional PCA (fPCA) (as in [42]), which were used to derive kinematic synergies. Optimization-based methods usually involve hypotheses on the motion generation that limit the variability of the planned movement. These methods generate humanlike motions, but they are only appropriate for simple point-to-point movements with a limited range of motion. So, they are unsuitable when applied to complex tasks like those of activities-of-daily-life (ADLs). To produce the greatest effect in robotic rehabilitation, exoskeleton robots require the online trajectory capacity to operate in a real environment. Trajectory planning methods in the first trajectory are unsuitable for unstructured environments like in the real world. This is why research groups have been interested in the second type of approach (Table 2), imitation-learning methods (LbD methods). These methods rely on trajectory learning, where robots learn human skills from demonstrations and later reproduce the movement through a trained model or a function approximation. Deconvolutional neural networks (DNN) (as in [10]), multilevel convolutional neural networks (as in [8]), and artificial neural networks (ANNs) (as in [18; 54]) are used for function approximation; Gaussian mixture models (GMM) (as in [14; 56]), hidden Markov models (HMM), and dynamic-motion-primitive (DMP) models (as in [11]) are used as models for upper-limb exoskeleton robots in the training phase. The training is achieved using expectation-maximization (EM) algorithms (as in [14; 56]) and the Levenberg-Marquart algorithm (as in [11; 54]). The LbD methods have the advantage of avoiding the calculation of the inverse kinematics. These methods have high computational costs, but this limit no longer exists once the learning phase is complete. However, demonstrations in joint space are strongly time-dependent. This issue is considered in the literature using methods based on dynamic time warping (DTW), which destroys the accuracy of the generated trajectories. [PERSON] et al. used Lloyd's algorithm to encode input signals and a modified HMM to more accurately plan trajectories in joint space. Although the study has not been tested on patients, we think that this method of generating the desired trajectory in joint space should be explored. Our opinion is motivated by two reasons: firstly, because there are few works in joint space; secondly, because trajectory learning is still unexplored for exoskeleton robots in comparison to policy learning. The studies presented in this review are summarized in Tables 1 and 2.