## 4 Discussion  
### Challenges in Trajectory Planning of Exoskeleton Robots  
Great advances in robotics have enabled the use of exoskeletons for functional movements with repeatability and intensity in rehabilitation and for assistive goals. In addition, with trajectory planning, their usage can be extended to home usage. Despite the advantages of these robotic devices, there are still challenges associated with their use. In this section, we discuss the challenges that make trajectory planning more difficult. Due to the physical coupling between the human body and the exoskeleton, typical strategies for determining the desired trajectory to be tracked by the exoskeleton during complex tasks consist of reproducing the movement of the human limb. However, it is difficult to accurately replicate human kinematics with robots because of the morphologic variability between individuals and the complexity of joint kinematics [59]. The differences between kinematic chains, referred to as \"kinematic incompatibility\", of human limbs and robots lead to hyperstaticity or overconstraint [60]. As a result, this can hinder the security and comfort of the user. In the literature, it was indicated that adding more DoFs into the configuration of an exoskeleton improves kinematic compatibility [61]. For this goal, there are two configurations--self-tracing and alignment-free exoskeletons of the joint axis (center)--that are exploited for upper-limb exoskeletons [62]. In the self-tracing configuration, an appropriate number of DoFs of active or passive joints are added in series into the main exoskeleton configuration. The alignment-free configuration consists of introducing an appropriate number of passive joints into the link between the exoskeleton and the user's upper limb. Both exoskeleton configurations present their own advantages and problems that are not addressed in this paper. With the aim of combining the benefits of both configurations, [PERSON], [PERSON] et al. recently proposed a 4-DOF self-aligning mechanism for upper-limb exoskeletons [60]. Moreover, the kinematic redundancy of the human arm poses challenges with respect to joint-space trajectory planning for upper-limb exoskeletons. The essence of the issue here is the inverse kinematics problem, whose solution is  
Figure 4: Adapted from [14]. Trajectory planning based on learning by demonstration. ADL: activities-of-daily-life; NN: neural network; ANN: artificial NN; HMM: hidden Markov model. complicated when the number of DoFs at the joint level exceeds one at the hand level. A review indicates that two approaches are typically exploited to resolve kinematic redundancy in exoskeletons [63]. In the first approach, angular excursions at the joint are minimized in some way. On the basis of this concept, some previous studies used methods based on the calculation of swivel angles [25; 47]. The second approach relies on the relationship between the degrees of freedom. In addition to these limits, two main challenges were identified in trajectory planning for exoskeleton robots [7]. The first is trajectory optimization [7; 10; 64], also known as the optimal-control problem [64; 65]; it is challenging to optimize a trajectory in order to suit a user's motion profile [66]. This difficulty results from user motion profiles being unique to the kinematics and dynamics of the wearer and to environmental settings. There are two approaches to solving the trajectory-optimization problem for exoskeletons, offline, and online trajectory optimization. In the online approach, there are two possibilities. The first is that optimization is run in the background, and the trajectory is periodically updated, leading to the low computational performance and poor reaction time of the trajectory planner. An alternative possibility consists of using a simplified model to accelerate calculation, but there is no guarantee of convergence since the definition of a trajectory-optimization problem entails the definition of the dynamic environment [64].