An Upper Limb Exoskeleton Motion Generation Algorithm Based on Separating Shoulder and Arm Motion

Many rehabilitation exoskeletons have been used in the field of stroke rehabilitation. Generating human-like motion is necessary for exoskeletons to help patients perform activities of daily living (ADL) while maintaining interaction quality and ergonomics. However, most of the current motion generation algorithms utilize inverse kinematics (IK) to solve the final configuration before generation, and do not consider the movement of shoulder girdle. Separately considering the shoulder girdle motion and arm motion, this paper proposes an algorithm integrated IK to generate human-like motion. The arm moves towards the target with a bell-shaped velocity in the absence of the final configuration, and the shoulder girdle maintain natural passive motion. Moreover, the generated motion can be mapped to the configuration space of exoskeletons. Compared with the experimental data collected using a motion capture system, the values of RMSE and HPDI of the generated wrist trajectory in the task space are within 0.2 and 0.17, respectively, while those of RMSE in the joint space are within 15 deg, which demonstrates the human-like nature of the generated motion.


I. INTRODUCTION
S TROKE has been a widespread and serious global health care problem, with the highest rate of disability for a single disease.There were 13.7-million new cases of stroke worldwide in 2016, and this number continues to rise [1].The most common and widely recognized impairment following stroke is motor impairment, and rehabilitation is an effective This work involved human subjects or animals in its research.Approval of all ethical and experimental procedures and protocols was granted by the Laboratory Academic Committee of the State Key laboratory of Robotics and System under Application No. 2023043, prior to the experiments.
Digital Object Identifier 10.1109/TNSRE.2024.3356724 way to help patients regain their motor abilities [2].To date, several rehabilitation robots have been developed to improve both motor control and strength in post-stroke upper extremity paralysis, which can help speed up neural remodeling significantly, and appear to be safe [3], [4], [5].One core requirement of rehabilitation robots is the capability of the system in producing natural and human-like movements [6], which is extremely important for patients with poor mobility in the early stage of hemiplegia.Generating human-like motion that can be adopted for upper limb exoskeletons is challenging for the following reasons: (1) Numerous joints in the upper limb bring two types of difficulties: upper limb modeling and kinematic redundancy [7].During ADL, delicate operations are carried out by the end of the upper limbs such as the wrist and fingers, while the remaining parts, which is the focus of this study, only serve to move the wrist to a convenient position for operation.When only considering the wrist position, degrees of freedom (DOF) are redundant.And the upper limb can present different configurations while maintaining the wrist and torso position.Due to the presence of swivel angles, the elbow is free to swivel about the axis from shoulder to wrist while maintaining the shoulder and wrist positions constant.However, shoulder strap movements change the shoulder joint position, and increase redundancy and complexity.Therefore, addressing the redundancy resolution problem is challenging.
(2) During ADL, the natural movements of the upper arm are strongly coordinated with the movements of the shoulder girdle, represented by the scapulohumeral rhythm (SHR).Without attention to the coordinated motion at the shoulder, joint instability may occur, resulting in shoulder pain or injuries including irritation and impingement of the rotator cuff [8].
(3) The planning of human motion integrates the process of IK.Given the target position, the upper limb starts moving from the start configuration with bell-shaped velocity profiles [9].The final configuration is unknown until arriving the target.With the same target but different start configurations, the final configurations may still be various.The planning of human motion is different from traditional generation algorithm which need IK to get the final configuration in advance.
Numerous methods have been developed for generating reference motion in exoskeletons.Mapping the motion of a healthy individual to configuration space of exoskeletons is a common approach [10], [11].Since the motion is generated off-line, it is not capable to adapt to change in an environment, and additional equipment is required to capture a healthy individual's motion.Some theories suggest that the human Central Nervous System (CNS) plans movements based on the principle of minimizing specific costs, such as minimizing motion jerk in task space [12], [13], [14], angular jerk [15], squared variation of joint torque [16], [17] and muscle effort [18], [19].How to choose the specific costs is not obvious, and it is indeed a very debated topic in literature [6].Learning from demonstration (LfD) is one of the most intuitive ways to obtain the trajectory of anthropomorphic motions [20], [21], [22].Some literature focus on the motion of shoulder girdle, Stefano et al. introduced the SHR into IK [23], Rana et al. obtained the final configuration that supports SHR using an optimization method and then generated motion using geodesics [24].These aforementioned methods need IK to get a unique final configuration in advance, which differs from the planning of human motion.Furthermore, most studies did not consider the motion of shoulder girdle, which will lead to discomfort for patients.
This paper introduces a human-like motion generation algorithm that integrated IK for upper-limb exoskeletons.The upper limb is modeled by analyzing the motion of each joint and the shoulder and arm motions are considered separately, which can reduce redundancy and complexity.The coordinated motion of the shoulder straps is predicted by a multiple-inputmultiple-output (MIMO) model whose input is the orientation of upper arm.The arm is modeled as a spatial two-link and its end moving towards the target with bell-shaped velocity profiles, ensuring similarity to that of human motion in the task space, while avoiding the torso.The generated motion of upper limb is mapped to configuration space of exoskeletons using a geometric transformation method.The generated motion considers the scapulohumeral rhythm (SHR) and subjects to the specifications of human planning, leading to different final configurations for the same target point from different start configurations without prior knowledge of the final configuration.The algorithm generates humanoid motion at the kinematic level, without involving dynamics.
Overall, the main contribution of this paper is: 1) A human-like motion generation algorithm which considers the SHR was proposed.A MIMO shoulder girdle motion prediction model which can predict elevation/depression and protraction/retraction angles of shoulder girdle based on the orientation of upper arm was proposed.It enables the generated motion to support SHR.
2) The generation algorithm which integrated IK can generate motion without prior knowledge of the final configuration.Even given the same target, the final configuration of the generated humanoid motion may be different with various start configurations.

II. UPPER LIMB MODEL
The shape of human torso is irregular.Due to the movement of upper limbs on the upper half plane in front of the torso, the shape of back and abdomen can be disregarded.The shape of Human upper limb model.The coral components are the models of shoulder straps.The blue ones are the models of arm.q SG1 and q SG2 represent the elevation/depression and protraction/retraction of the shoulder girdle, respectively.ϕ po and ϕ az represent the elevation/depression and protraction/retraction of the upper arm, respectively.the human torso is symmetrical about the sagittal plane, and can be modeled using a hyperquadric surface [25] which is symmetrical about the horizontal plane passing through the thickest part of the torso and the sagittal plane: where the parameters a 1 , a 2 , and a 3 represent the length, width and height of the torso, respectively.(x 0 , y 0 , z 0 ) represents the center of the torso.ε 2 determines the shape of the superellipsoid cross section parallel to the (x, y) plane, while ε 1 determines the shape of the superellipsoid cross section in a plane perpendicular to the (x, y) plane and containing z axis.By changing these five parameters, human torsos of different sizes can be modeled.
It is difficult to analysis the kinematic of human upper limb because of various joints involved.Shoulder girdle is made up of four joints (sternoclavicular, acromioclavicular, glenohumeral, and scapulothoracic) and three bones (clavicle, scapula, and humerus) [26].Upper arm is connected to the torso by glenohumeral (GH) joint.Forearm is connected to the upper arm by elbow joint which is a hinge joint made up of three bones.It's difficult and unnecessary to analyze the motion of each bone.The motion of upper limb can be separated into the motion of the shoulder girdle and arm.
The upper limb can be modeled by analyzing the motion of shoulder girdle and arm.The motion of shoulder girdle results in translational motions of the GH joint, such as elevation-depression and protraction-retraction.The model of shoulder girdle can be built by analyzing the motions of the GH joint.According to the findings, the trajectory of the GH joint falls in two circular arcs during elevation-depression and protraction-retraction.The distance between the rotation axis of two arcs deviate only<3 mm [27].The shoulder girdle can be modeled with two mutually orthogonal revolute joints.The ball-and-socket GH joint enables a wide range of movement in the shoulder.GH joint is kinematically equivalent to a serial chain with three rotational joints whose axes intersect at a single point.For simplicity, set the three axes to be orthogonal to each other.The elbow joint allows for flexion and extension of the forearm.The forearm's rotation along the longitudinal axis of itself is ignored because it is independent of wrist position.The elbow joint can be modeled as a revolute joint whose axis is perpendicular to the plane formed by the upper arm and forearm.The upper limb of human is modeled as shown in the Fig. 1 and Table I.
The motion model of the upper limb of satisfies the following equations: where x w is the position of the wrist, q is the configuration of the upper limb, q = q SG , q .q SG is the configuration of shoulder girdle, while q is the configuration of arm.f and f −1 are the forward and inverse kinematics functions.

III. MOTION GENERATION ALGORITHM BASED ON SEPARATING SHOULDER AND ARM MOTION
Studies have shown that ADL training is effective in the recovery of patients [28].However, in the early stage of rehabilitation, patients cannot complete these tasks alone, exoskeletons can generate motion to assist patients [29].Motion generation algorithm that supports SHR and integrated IK is considered in this work.During the large ROM of upper limb, the center of the GH joint will passively move with the lift of the upper arm.This phenomenon always exists in movements.Therefore, it is necessary to integrate the relationship into the algorithm that generates upper limb motion.The movement of arm can be considered to be active, while the movement of the shoulder girdle is passive.Therefore, the motions of the two can be handled separately.

A. Motion of Shoulder Girdle
The movement of upper limb is characterized by a coordinated motion of the shoulder.As the humerus of the upper arm moves, the shoulder girdle in such a way that a non-linear relationship is maintained between the humerothoracic elevation and shoulder girdle elevation.As a result, the center of rotation of the GH joint moves along with the subject, and must thus be followed accurately by the exoskeleton.
This nonlinear relationship between the humerothoracic elevation and shoulder girdle elevation is usually fitted with a polynomial.However, this description is not comprehensive.In addition, the movement of shoulder girdle is also associated with ϕ az in the Fig. 1.The relationship of humerus orientation and scapulohumeral configuration can be abstracted as a MIMO model.However, it is not currently applied in the human joint angles prediction domain.Xu presented a MLS-SVR Multi-output algorithm [30], in multi-output setting with strong generalization capability.Considering the limited amount of data and the requirement for a smooth fit, MLS-SVR was chosen as a predictor of the rotation angles of the shoulder girdle.The multi-output regression is regarded as finding the mapping between an incoming vector x = ϕ po , ϕ az and an output vector q SG = q SG1 , q SG2 , which can be described as an optimization problem as follows: min where n is the number of types of input variables, m is the number of data elements, V is a n × m weight matrix, î is a m × 1 unit vector, is a matrix n × m consisting of slack variables, λ is a positive real regularized parameter, and b is a m × 1 vector that minimizes the objective function.Z = (ϕ (x 1 ) , ϕ (x 2 ) , . . ., ϕ (x l )), and ϕ is a mapping to another Hilbert space.And the corresponding decision function for the multiple outputs is: where κ(x, y) = exp − p∥x − y∥ 2 , p > 0, is the radial basis function and α is the coefficient consisting of Lagrange multipliers.This approach can be used to predict the configuration of shoulder girdle.The relationship between the movement of shoulder girdle and orientation of upper arm can be described correctly by the MIMO prediction model.During the process of generating motion, motion of shoulder girdle is predicted by the MIMO model.It takes the coordinated movement of shoulder girdle into account in motion generation which will reduce the uncomfortable of patients.Next, only the movement of arm needs to be considered.This method of separating shoulder and arm motion reduces the complexity of generation algorithm.

B. Motion of Arm
After predicting shoulder girdle motion using the MIMO model, only the arm motion needs to be considered.Arm can be regarded as a spatial two-link with four DOF.The first link is upper arm, which links to the torso by GH joint.The second link is forearm, which links to the first link by elbow joint.The spatial two-link with four DOF is redundant when only focusing the position of the wrist.
The configuration of the spatial two-link, described by the 4-dimensional vector q, is related to the end-effector (wrist) position, denoted by the 3-dimensional vector xw whose frame is located in GH joint, by the following equations: (5) where J is the 3 × 4 Jacobian matrix, J # is the generalized inverse of J and N is a matrix representing the projection into the null space of J, N = I − J # J [31].
To mimic the motion of human, end of the spatial two-link which represents wrist moves towards the target with bell-shaped velocity profiles from the start configuration.The final configuration is only known when the target is reached.During ADL, the upper limb of human will not collide with torso.Similarly, to ensure the safety of the person wearing exoskeletons, the motion generated by algorithm should avoid collisions with torso.As the spatial two-link is redundant, it can perform more tasks which can be broken down into several subtasks with different priority [32].In our case, the task with the highest priority, referred to as the main task, is moving the wrist towards the target, while the other subtask is related to avoiding collisions with torso.
Upper arm can be modeled as a cylinder with a radius equal to the maximum radius of the upper arm and a length equal to the length of the upper arm.The distance between the upper arm and torso is simplified as the distance between the hyperbolic paraboloid and axis of the cylinder minus the radius of the cylinder.The distance between a quadric surface and a straight line in space cannot be computed in closed form, using the method of traversal instead.Only the collisions between the upper arm and torso are considered because routine reaching or grasping tasks rarely involve collisions between forearm and torso.In addition, when the target point is on the torso, the distal end of forearm comes in contact with the torso.A blind zone, which does not need to consider collisions, is added to the upper end of the arm because this zone is the part connecting the arms and torso via GH joint.
Denote the corresponding closest point on the upper arm as the "critical point", in Fig. 2 marked with A o .To avoid a possible collision, one method is to assign to A o a velocity that it moves away from the torso as it is proposed in [9].The motion of the wrist and the critical point can be described by equations: J o is the Jacobian in point A o defined in the Cartesian space.We can find a common solution for both equations by combining ( 6) and ( 8): The first term J # ẋw guarantees the joint motion necessary for the desired wrist velocity.The rest, i.e. the homogeneous solution represents the motion of the point A o .
In fact, the torso avoidance requires only the motion in the direction of the line connecting the critical point and the closest point on the torso.Let d o be the vector connecting the closest points on the torso and upper arm (see Fig. 2).The Jacobian, which relates the joint space velocities q and the velocity in the direction of d o , can be calculated as n o is the unit vector in the direction d o , given by As upper arm often moves near the torso during ADL, it is not necessary to assign a velocity to move upper arm away from the torso.We just need upper arm decelerate when it nears to the torso.A deceleration zone can be added to the upper limb as it approaches the torso.When in this zone, the closer the critical distance to the torso, the slower the speed, and when it is very close, the movement can come to a stop for safe.Set the ẋo equal to 0, rewrite an obstacle avoidance algorithm proposed in reference [33]: α h can change the amount of the homogenous solution for smoother motion, which been selected as where d m and d i represent the distance between the torso and the inner and outer edges of the deceleration zone.The algorithm calculates the positions of the upper arm based on the joint angles of the human body model at each moment using forward kinematics.It determines the point on the upper arm closest to the superquadric surface representing the torso, which called "critical point".When d i ≤ ∥d o ∥, α h is 0, and the obstacle avoidance algorithm does not work, only considers the motion of wrist.When the upper arm moves closer to the torso and enters the deceleration zone d m < ∥d o ∥ < d i , the obstacle avoidance algorithm begins to work.Due to the presence of null space, while ensuring wrist movement, the closer the distance, the slower the speed at which the critical point approaches the torso.Until the critical point reaches the inner edges of the deceleration zone, α h is 1, and the critical point does not approach the torso.

C. Motion Generation Algorithm
The arm is modeled by a spatial two-link to perform the main task of tracking bell-shaped velocity profiles to reach the target point, and at the same time perform the subtask of obstacle avoidance far away from the torso.During the movement of upper arm, the orientation of upper arm is recorded, and shoulder girdle passively move according to the established MIMO model.

Algorithm 1 Motion Generation Algorithm Based on Separating Shoulder and Arm Motion (SSA)
Input:

IV. TRANSFORMATION OF CONFIGURATION BETWEEN
HUMAN MODEL AND EXOSKELETON After completing the motion generation algorithm of upper limb, it needs to be implemented on the exoskeleton.

TABLE II DH PARAMETERS OF FREE
Therefore, the algorithm needs to be transformed from the configuration space of the human body model to the configuration space of the exoskeleton.FREE [34] is a seven degree of freedom exoskeleton, supports the movement of the shoulder girdle, the GH and elbow joints, even the rotation along the longitudinal axis of forearm.The DH parameters of FREE are shown in Table II.It has geometric equivalence for anthropomorphic arms (GEAA) as shown in Fig. 3, which can be used for the conversion between two spaces.The position of Free's GH joint should coincide with that of the human: Due to the same parameters of the shoulder strap of the exoskeleton as that of the upper limb model, the first two joint angles of the exoskeleton q e 1 , q e 2 can be get: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
For exoskeletons with different shoulder strap designs, a transformation may be required before calculation.
The orientation of the upper arm can be obtained through the position of the GH and elbow joints, which is the same as the orientation of the link 6 of the exoskeleton.The position of the GH and elbow joints is obtained through forward kinematics of human upper limb model.
The axis of the elbow joint needs to coincide with the FREE, which must be perpendicular to the plane formed by the upper arm and forearm: Based on the DH coordinate assignment, z 5 is co-located on a plane formed by the axis of rotation of elbow z 6 , and e a .z 5 can be obtained by rotating an angle β 3 around the normal vector of the plane n: z 3 can be obtained by z 4 can be determined by using three constraints, given that z 4 is a unit vector that makes an angle of β 2 with z 3 and an angle of β 3 with z 5 .
According to the DH criterion, after obtaining z i , the x i can be obtained, which is perpendicular to the plane formed by z i and z i+1 .
Then q e i equal the angle between x i−1 and x i : Transformation only requires the position of the GH joint center, elbow joint, and wrist.Therefore, the configuration of exoskeletons can also be obtained by upper limb joint position which are obtained by motion acquisition system.Unlike conventional IK algorithms which involve solving nonlinear equations, this method is simpler and more efficient yet requires more information about joint position.The proposed approach shares similarities with the method outlined in literature [24], but modifies the calculation of z 5 and z 6 , reduces the number of equations to be solved.The proposed approach shares similarities with the method outlined in literature [24], whose exoskeleton has also same GEAA with different design of shoulder.The calculation of z 5 and z 6 is modified, which reduces the number of equations to be solved.Notably, the use of a cross product operation to solve for z 6 helps mitigate the issue of skin slippage when joint position is obtained by motion acquisition system.

V. EXPERIMENTAL SET-UP AND RESULTS
To evaluate the effectiveness of the proposed motion generation algorithm, motions of healthy subjects performing a class of ADL were captured with a motion capture system and compared with the algorithm outputs.To train predictive models in section III, shoulder girdle kinematic data of healthy subjects were recorded using the same system.In order to complete the torso avoidance algorithm, the subjects' body information needs to be measured.The motion capture system used consisted of 8 cameras (Mars2H, Nokov, sampling rate 60 Hz) and reflective markers.

A. Subject Data Collection
Five healthy right-handed subjects, on average 24 years old, with no history of upper limb impairment, voluntarily participated in the experiments.The experimental protocol was approved by the Laboratory Academic Committee of the State Key Laboratory of Robotics and System (Ref.No.2023043) prior to the experiments.Each subject is informed of the experimental procedure and gives consent prior to the start of the experiment.Before the experiment begins, measurements of the subjects' torso shape parameters, clavicle length, arm circumference and upper and lower arm lengths are taken.The information of subjects is shown in Table III.The experiment requires subjects to perform specific actions while keeping their torso still.Using two-sided adhesives, nine reflective markers were attached to the subjects' skin according to a standard marker placement method as shown in Fig. 4a.Shoulder center was determined as the centroid of the 3 markers on the shoulder.
Subjects need to perform 5 types of ADL tasks: drinking water, touching ear on the same side of the body, washing (touching shoulder on the opposite body), touching forehead and reaching cup located on the platform.Each task starts from three different start configurations as shown in Fig. 4g, so a total of 15 motions were performed.Each movement needs to be repeated ten times.
Recording the position of reflective markers attached to the subjects' body when they perform ADL tasks, the motion of subjects in task space is obtained.The motion in joint space is calculated using the method in Section IV, and then compare with the motion generated by the algorithm.

B. Performance Verification
Given the same start configuration and target position as Section V-A, motion will be generated by the algorithm.In order to validate the effectiveness of the algorithm, the motion will be compared to the subjects' motion also motion generated with other algorithms.As most existing human-like motion generation algorithms are implemented with a known final configuration or ignore the motion of shoulder girdle.Therefore, they cannot be compared with the proposed algorithm, which considers the motion of shoulder girdle and integrated IK.We compare our Separating Shoulder and Arm Motion algorithm (SSA) with SSA ignore torso collisions (SSAITC).
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.To validate the effectiveness of the algorithm, comparisons are made between the experimental data in the task space and the joint space, respectively.The similarity of the task space is evaluated by the root mean square error (normalized by motion length) and the Hand Path Deviation Index (HPDI) values.Divide the maximum value of the minimum Euclidean distance between the measured path and the predicted path by the path length to get the value of HPDI, with higher values showing less resemblance [35].The root mean square error is also calculated in the evaluation of joint space.In addition to evaluating the differences between the algorithm and experimental data in the joint space of motion planning process, it is also necessary to discuss the differences in the final configurations, as the proposed algorithms integrate IK and does not require prior knowledge of the final configurations.

TABLE III SUBJECTS CHARACTERISTICS
Table IV provides a comparison of the 3D wrist paths obtained through experiments and those generated by the proposed algorithm using SSA and SSAITC for randomly selected participants' 5 classes motions.Fig. 5 and Fig. 6 show two examples of comparison in joint space respectively.Solid blue lines represent the experimental data, while the yellow and blue dashed graphs show SSAITC and SSA outputs.Meanwhile, Table V presents a quantitative evaluation of the joint space paths generated by the algorithm and their correspondence with the randomly selected experimental data.Additionally, Fig. 7 assesses the similarity of the final   the torso avoidance algorithm is implemented in the null space, the motion of avoiding torso does not affect the motion of wrist.Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE V JOINT SPACE QUANTITATIVE MEASURES: RMSE MEAN ±STANDARD DEVIATION
The joint motion generated by two algorithm is similar to the experimental data, especially q SG1 , q SG2 and q2 .The performance of the two algorithms is almost identical as the torso avoidance algorithm did not come into effect during the drinking motion.Fig. 6 shows a typical example for washing from start configuration II in joint space.At the beginning of generating motion, the two algorithms performed consistently until the torso avoidance algorithm began to take effect in the latter half, and SSA algorithm performed better.Table V also validates the similarity between the motion generated by the algorithms and the experimental data in the joint space.
Even with the same motion target, the change of start configurations will lead to different final configurations, as shown by the yellow bars in Fig. 7.The final configurations generated by the algorithms can track these differences.For motions that may collide with the torso such as washing, the final configuration generated by SSA is significantly better than SSAITC.
The output of motion generation algorithm needs to be mapped into configuration space of exoskeletons by the geometric transformation method.The method of configuration transformation between human model and exoskeleton utilizes the geometric equivalence of two configurations: (1) the GH, elbow, and wrist joints of the human body model overlap those of the exoskeleton in task space, respectively; (2) and their upper arm vectors are identical.Fig. 8 shows a washing motion of human model in top left, while the equivalent transformed motion to the exoskeleton joint space using GEAA is depicted in top right.In the bottom left corner, the angle between the two upper arm vectors is shown, demonstrating that the directions of two upper arm vectors are aligned.In the bottom right corner, the positions of the GH joint, elbow joint, and wrist joint in the task space for the two configurations also substantially overlap, affirming the effectiveness of the transformation.
As another contribution of this paper, the effect of MIMO model used to predict the movement of the shoulder girdle is presented in Fig. 9. From the figure, it can be seen that the model can track the movement of the shoulder girdle very well.The error between predicted angle and actual data is within 0.05 radians.

VI. DISCUSSION
In the early stages of rehabilitation, the use of exoskeletons to generate human-like motion to guide patients perform ADL is highly appealing.An increasing number of exoskeletons supports shoulder girdle movements with active joints.This design ensures that the wearer can engage in a wide range of movements without discomfort caused by misalignment of joint centers.However, it also poses challenges in IK and motion generation.Describing SHR accurately and supporting SHR in the generated motions remains a difficulty in motion generation.The redundancy of the upper limbs and collaborative motion between joints caused by SHR present challenges in both IK and motion generation.Additionally, the redundancy of the upper limb results in a phenomenon where different start configurations lead to varying final positions when individuals reach the same goal while performing activities of daily living (ADL).This phenomenon involves the problem of IK solution selection.

A. Benefits
The motion generation algorithm based on separating shoulder and arm motion divides the kinematic chain into segments, with one segment supporting shoulder girdle movement and another segment supporting arm movement.This reduces the number of DOF which need control, thereby reducing the complexity of the problem.The shoulder girdle segment predicts the motion of shoulder girdle by a MIMO model trained with wearer's motion data.Compared to fitting with a general polynomial, the prediction is more accurate.The kinematic chain of arm starts from GH joint, and moves toward target position with bell-shaped velocity profiles from start configuration while avoiding collision with torso.In each iteration, the shoulder girdle movement is predicted based on orientation of upper arm, updating the position of the GH joint, and the arm continues to move from current configuration towards the target position with the new position of the GH joint.This ensures that: a.The entire process of generate motion supports SHR.b.The generation algorithm integrated IK avoids the problem of difficulty in IK caused by SHR.
c. Since the start configuration is taken as the initial condition for each motion generation, which will influence the final configuration, the phenomenon of different final configurations caused by different start configurations is realized.
d. Avoiding the torso is one of the planning objectives, ensuring the safety of the wearer.
Training the MIMO model for SHR is time-consuming, and was conducted offline.The motion generation takes less than 0.5 seconds on a commercial computer (Intel i9-12900H and 16G RAM) in MATLAB, and it can be even faster in an embedded system, which meets real-time requirements.

B. Limitations and Future Work
To ensure that exoskeleton does not collide with torso when it completes the generated motion, it is inaccurate to use hyperquadric surface to fit the torso shape.When generating motion, a lack of perception and understanding of the environment is detrimental to completing ADL tasks, such as the perception of the position of the water cup while drinking water.In addition,we only conducted experiments on healthy subjects and did not test the algorithm's effectiveness on patients with a history of stroke.
In future work, depth cameras will be used to perceive environment and obtain precise distance between torso and upper arms for torso avoidance algorithms.Conducting trials with patients is also one of our future tasks.

VII. CONCLUSION
Based on separating the shoulder girdle and arm motion, a motion generation algorithm was developed to support the SHR and integrated IK.The shoulder girdle moves passively according to the orientation of the upper arm, and the arm is modeled as spatial two-linkages whose end moves towards the target with bell-shaped velocity profiles without the knowledge of final configurations.The generated motion is then transformed into the configuration space of a six-degree-of-freedom exoskeleton by means of GEAA.The generation motion is highly similar to nature upper limb motion.Compared with the experimental data collected by the motion capture system, the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
values of RMSE and HPDI of the generated wrist trajectory in the task space are within 0.2 and 0.17, respectively, while those of RMSE in the joint space are within 15 deg.Describing the SHR as a MIMO model allows for precise tracking of shoulder girdle motion, which the error is within 0.05 radians.Finally, the transformation method GEAA can not only be used to converse the human and robot configuration space, but also to estimate joint angle with the information obtained by the motion capture system.

Manuscript received 22
August 2023; revised 31 October 2023 and 30 November 2023; accepted 16 December 2023.Date of publication 22 January 2024; date of current version 14 March 2024.This work was supported by the Major Research Plan of National Natural Science Foundation 471 of China under Grant 91648106.(Jiajia Wang and Shuo Pei contributed equally to this work.)(Corresponding author: Yufeng Yao.)

Fig. 1 .
Fig. 1.Human upper limb model.The coral components are the models of shoulder straps.The blue ones are the models of arm.q SG1 and q SG2 represent the elevation/depression and protraction/retraction of the shoulder girdle, respectively.ϕ po and ϕ az represent the elevation/depression and protraction/retraction of the upper arm, respectively.

Fig. 2 .
Fig. 2. Diagram of arm motion.The sapphire area represents a blind spot that does not consider collisions.The red area represents the deceleration zone surrounding the torso.The upper right corner features a sectional view of a plane passing through the critical point parallel to the horizontal plane.

Fig. 3 .
Fig. 3. Transformation of configuration between human model and exoskeleton.

Fig. 5 .
Fig. 5. Comparison between randomly selected experimental data (-blue) and algorithm outputs (-.yellow for SSAITC, and--blue for SSA) for drinking from start configuration I in joint space.

Fig. 6 .
Fig. 6.Comparison between randomly selected experimental data (-blue) and algorithm outputs (-.yellow for SSAITC, and--blue for SSA) for washing from start configuration II in joint space.configurationsbetween the algorithm and randomly selected experimental results.As the TableIVshows, the values of RMSE of wrist trajectory in task space are within 0.2 and most of the data are around 0.1.Most of the values of HPDI are around 0.1, with only a few exceeding 0.15.It can validate the similarity between the motion generated by the algorithm and the experimental data in the task space.There is little difference between the two algorithms in terms of the similarity between wrist paths and experimental data in the task space.Because

Fig. 7 .
Fig. 7. Final configurations of ADLs from I,II, and III start configurations.

Figure. 5
Figure. 5 shows a typical example showing the comparison between randomly selected experimental data and algorithm outputs for drinking from start configuration I in joint space.

Fig. 8 .
Fig. 8. Validation of configuration transformation between human model and exoskeleton.

Fig. 9 .
Fig. 9. Comparison of actual and predicted angles of shoulder girdle motion during drinking from start configuration I.