## 1 Introduction  
Developments in assistive robotic devices offer enormous prospects in medical fields, such as surgical, rehabilitation, and assistive robotics [1]. Many robotic devices, referred to as exoskeletons, have been developed for patient rehabilitation and physical assistance. Their efficacy has been proved in these fields. For instance, rehabilitation robots interact with humans and can be successfully employed in the early phase of recovery from stroke [2; 3; 4; 5], but despite great progress, this introduces the trajectory-planning problem, which is fundamental and widely dealt with in robotics. Indeed, in any autonomous robotic system, trajectory planning is of crucial importance in moving the robot from its initial position to the desired position because it finds the desired trajectory linking the two positions or configurations (start and goal). In robotic systems such as exoskeleton robots, the motion planner generates the desired trajectory, and the control algorithm ensures that the robot tracks this planned trajectory (see Figure 1). Consequently, trajectory planning is an essential tool for understanding and fine-tuning exoskeleton control. Because of the close physical interaction between exoskeletons and humans, the problem of planning suitable trajectories is more relevant for their usage in order to ensure user safety and comfort. Initially, exoskeletons were applied in rehabilitation for training rather than to help therapists to perform training on patients. Even if their effect was satisfactory, this method required the presence of the therapist [3; 6]. Moreover, this approach restricted applications to clinical use. Currently, when using exoskeleton robots to assist rehabilitation therapy, the motion trajectory for training the user's limb movements first needs to be planned. With an appropriate trajectory-planning method, exoskeletons can operate in realistic environments, such as those of daily life [7]. Accordingly, proper trajectory planning is essential to the use of exoskeleton robots in home settings. Much work was done on trajectory planning for exoskeleton robots [8; 9; 10; 11; 12; 13; 14; 15]. In this context, this paper deals with trajectory-planning problems, i.e., the computation of desired motion profiles for the actuation system of automatic machines. We explore methods of trajectory planning used in the literature for upper-limb exoskeleton robots. In robotics, trajectory planning can either be done in task space or in configuration space for exoskeletons [16]. When trajectory planning is done in task space, inverse kinematics is required to obtain joint motion. However, it is difficult to solve the inverse kinematics problem because there is an infinite number of solutions [17]. Attempts to resolve the inverse kinematics problem in robotics have used many approaches, including Jacobian [12], optimization, dimensionality-reduction, and learning-based methods [18]. In [19], a method based on optimization was proposed to implicitly resolve inverse kinematics. In addition, since exoskeleton control is done at the joint level, trajectory planning in joint space makes it possible to avoid the calculation of inverse kinematics. Most planning methods in joint space rely on learning human behavior and the transfer of human skills to the robot through demonstration. However, demonstrations in joint space are strongly time-dependent [16]. Although methods/algorithms based on dynamic time warping (DTW) exist to deal with the time-dependence problem (as in [14]), their accuracy is low when applied to approximate high dimensions. In addition to the above challenges, environmental changes related to activities-of-daily-life (ADL) task scenarios add difficulties in trajectory planning. Because of these challenges and the large number of papers in the field of exoskeleton control, this paper addresses the trajectory-planning problem. The purpose of this literature review is to explore trajectory-planning methods for exoskeleton control, especially for the upper limbs.