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Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 7847014, 10 pages https://doi.org/10.1155/2018/7847014 Research Article Qiming Chen , Hong Cheng , Chunfeng Yue, Rui Huang , and Hongliang Guo Center for Robotics, School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, China Correspondence should be addressed to Qiming Chen; [email protected] Received 22 January 2018; Accepted 23 May 2018; Published 2 July 2018 Academic Editor: Dongming Gan Copyright © 2018 Qiming Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Purpose. Powered lower-limb exoskeleton has gained considerable interests, since it can help patients with spinal cord injury(SCI) to stand and walk again. Providing walking assistance with SCI patients, most exoskeletons are designed to follow predeﬁned gait trajectories, which makes the patient walk unnaturally and feels uncomfortable. Furthermore, exoskeletons with predeﬁned gait trajectories cannot always maintain balance walking especially when encountering disturbances. Design/Methodology/Approach. This paper proposed a novel gait planning approach, which aims to provide reliable and balance gait during walking assistance. In this approach, we model the exoskeleton and patient together as a linear inverted pendulum (LIP) and obtain the patients intention through orbital energy diagram. To achieve dynamic gait planning of exoskeleton, the dynamic movement primitive (DMP) is utilized to model the gait trajectory. Meanwhile, the parameters of DMP are updated dynamically during one step, which aims to improve the ability of counteracting external disturbance. Findings. The proposed approach is validated in a human-exoskeleton simulation platform, and the experimental results show the eﬀectiveness and advantages of the proposed approach. Originality/Value. We decomposed the issue of obtain dynamic balance gait into three parts: (1) based on the sensory information of exoskeleton, the intention estimator is designed to estimate the intention of taking a step; (2) at the beginning of each step, the discrete gait planner utilized the obtained gait parameters such as step length S and step duration T and generate the trajectory of swing foot based on S, T ; (3) during walking process, continuous gait regulator is utilized to adjust the gait generated by discrete gait planner to counteract disturbance. interest from both academic researchers and industrial 1. Introduction entrepreneurs [3–5]. SCI is a temporary or permanent damage to the spinal cord On the development of lower-limb exoskeletons for that changes its function and might cause loss of muscle walking assistance, comfort and safety are two essential fea- function and sensation. According to the survey of the World tures. Many eﬀorts are made on the development of lower exoskeletons for walking assistance. Yan et al.[6] suggest that Health Organization [1], between 250,000 and 500,000 peo- ple are suﬀering from SCI every year around the world. SCI most of the exoskeletons for assistance still employ prede- patients who are forced to be bedridden and wheelchair ﬁned trajectories based on oﬀ-line simulations or captured bound are susceptible to developing decubitus, loss of bone human gait data. The generated reference patterns are gener- density, articular contracture of the lower limbs, and deep- ally tracked by position controllers of powered joints. It vein thrombosis [2]. Gait support using an exoskeleton robot forces patients to move with exoskeletons and lead uncom- may be an eﬀective way to address the abovementioned prob- fortable experience. Moreover, with predeﬁned trajectories, lems because a patient wearing the robot moves their legs exoskeletons and patients cannot keep balance when encoun- actively and the ground reaction force stimulates the sensory tering a disturbance. Therefore, for obtaining dynamic bal- and musculoskeletal system. Furthermore, the gait support ance gait, we consider both when to step and how to step. has a particularly meaningful role in the regaining of walking For when to step, various human-machine interfaces function in several SCI patients. Therefore, lower-limb (HMI) are designed. In [7], electromyography (EMG) signal exoskeletons are designed to provide movement assistance is utilized to get the intention of patients. However, it is dif- for people suﬀering SCI and have attracted increasing ﬁcult to measure EMG signal for patients with SCI motion 2 Applied Bionics and Biomechanics The mathematical relation between ZMP and physical stiﬀ- features such as tilt of torso [8] and upper arms [9] are utilized to obtain the intention of walking and trigger a ness is described with this model. Moreover, ZMP is regarded step. Center of mass (COM) based approaches are also as conditions of stability. Thus, for keeping balance desired, employed in HAL [10] and MINDWALKER [11, 12]. ZMP is served with the stiﬀness of joint actuators. However, these approaches are only based on observed Reference [16] shows that in dynamic balance, the condi- information and the experience of system designer Thresh- tion for static balance which says the projection of center of olds in these approaches must be adjusted manually for mass (CoM) should be within the support polygon is not suf- diﬀerent patients and situations. ﬁcient and turns out to be instantaneous capture point (ICP) For how to walk, many dynamic gait planning approaches should be within the support polygon. The paper [17] pre- are proposed. In [10], the exoskeleton changes the speed of sents a balance control for a powered lower-limb exoskeleton swing foot dynamically according to duration of support based on the concept ICP and implement it on the exoskele- phase for improving the experience of patients. However, ton named EMY-Balance (CEA-LIST). Joint torques for the balance of exoskeleton is not considered in this research. In speciﬁc actuation of EMY-Balance is computed to keep the [11, 12], extrapolated center of mass (XCoM) [13] method ICP in support polygon. is proposed to prevent the MINDWALKER exoskeleton In these approaches, ankle joints are needed to be actu- from falling sideways by online adjusting the step width ated. However, for portability in most of the exoskeletons (hip ab/adduction). However, disturbance in sagittal plane for SCI patients, ankle joints are not actuated. is not taken in account. 2.2. Stepping Approach. Stepping approach is widely utilized In this paper, we proposed a dynamic balance gait approach to obtain balance gait pattern for lower-limb exo- in balance control for humanoid robots [18, 19] and exoskel- skeleton. We model the human-exoskeleton system with lin- etons [11, 12, 20]. MINDWALKER [11, 12] is a powered lower-limb exoskeleton designed for paraplegics to regain ear inverted pendulum (LIP) and design the intention estimator based on the concept of orbital energy diagram. locomotion capability. It has ﬁve DOFs at each leg, with hip ﬂexion/extension and adduction/abduction and knee ﬂex- Discrete gait planner (planning a gait at the beginning of each step) and online gait regulator (online adjust the gait during ion/extension powered by SEAs, while hip rotation and ankle step taking) are proposed for achieving balance gait. The tra- pronation/supination passively sustained with certain stiﬀ- ness. Finite state machine (FSM) is deﬁned with various jectory of swing foot is modeled with DMPs, which can be adjusted dynamically and smoothly. In discrete gait planner, states and state transitions can also be triggered when the user manipulates the CoM position of the user-exoskeleton we utilize an optimization method with targeting orbital energy to obtain parameters of a gait trajectory. In online gait system. A trigger to initiate a step will be generated when regulator, we adjust DMPs dynamically for counteracting the the projection of the sagittal and lateral CoM positions on the ground fall in the desired quadrant. disturbance during a step. Hence, our contributions are twofolded: ﬁrst, our To prevent the user-exoskeleton from falling sideways, MINDWALKER implements online correction of the step approach enables exoskeleton walk as the intention of patients. Secondly, our approach obtain gait trajectories and width by adapting the amount of hip ab/adduction needed adjust it dynamically to stabilize balance during walking. during the swing phase. The required adjustment of hip joints is determined using XCoM [13]. If the user-exoskeleton sys- Experimental results in simulation environment show the eﬀectiveness and advantages of the proposed method. tem falls towards one side due to external perturbations such as being pushed at the shoulder or internal perturbations such as user’s upper body motion, the foot placement is adjusted 2. Literature Review resulting in a wider or a narrower step width to counteract such perturbations. However, this XCoM approach does Although predeﬁned trajectory approach is utilized in most not take the adaptation of sagittal plane in count. of exoskeleton for SCI patients, some attention is paid on In [20], gait planning for balance is based on ZMP. technologies for obtain balance gait patterns. In this section, 7-links model [21] is utilized to model exoskeleton. Trajecto- we will lay down the related works about technologies and ries of hip, knee, and ankle are modeled by parameters. lower limb exoskeleton systems for keeping balance during These parameters are obtained by optimal algorithm with walking. Some biomechanics researchers reveal several targeting ZMP. However, this approach is based on the approaches balance recovery of humanoid robots [14]. These 7-links model which is too complex for exoskeleton. approaches can be divided into two categories: internal joint approach and step taking approach. These approaches also have been used for balance control of exoskeletons. 3. Dynamic Balance Gait 2.1. Internal Joint Approach. Joints of exoskeletons are con- In this section, we will introduce the dynamic balance gait trolled to serve some crucial features of balance like zero approach. We ﬁrst present the framework of this approach moment point (ZMP) for internal joint approach. In [15], followed by the details of subsystems. for real-time balance control, variable physical stiﬀness actu- ators were implemented to exoskeletons. An abstracted biped 3.1. Framework for Dynamic Balance Gait. On the develop- model, torsional spring-loaded ﬂywheel, is utilized to capture ment of lower-limb exoskeletons for SCI patients, most of approximated angular momentum and physical stiﬀness. their ankle joints are passive (without actuators). Therefore, Applied Bionics and Biomechanics 3 we proposed a novel gait planning approach in this paper where r is the position of point mass (M) and θ is the angle of which based on the stepping strategy and the LIP model. LIP with ground. f denotes force applied along the LIP. g is Figure 1 shows the framework of proposed dynamic bal- gravity constants. With f = Mg/cos θ and τ =0, the point ance gait strategy, which decomposed into three parts: mass is kept on a horizontal line as Mx = f sin θ . In this intention estimator, discrete gait planner, and continuous situation, motion of point mass can be written as: gait regulator. The gait is divided into single-support phase and double- x = x, 2 support phase during normal walking. In single-support phase, the upper body of the human-exoskeleton system is where x and z is the position of point mass in XOZ plane. controlled by hip joint of stand leg, which should keep torso Thus, given initial conditions x and x , we can get the equa- 0 0 stay vertical. Therefore, the gait of human-exoskeleton sys- tion motion of CoM as follows: tem can be expressed as foot trajectories of swing leg. We model the trajectories of swing foot with DMPs, which can t t xt = x cosh + T x sing , be learned with sample trajectories of healthy people and 0 c 0 T T c c adjust gait trajectories online smoothly. Based on the LIP model and gait description with DMPs, three fundamental x t t xt = sinh + x cosh , parts in Figure 1 are employed to achieve dynamic balance T T T c c c gait. According to sensory information of exoskeleton, the intention estimator is designed to estimate the intention of where T is g/z. taking a step. At the beginning of each step, the discrete gait 3.3. Intention Estimator for Taking a Step. Walking with planner utilized the obtain trajectory of swing foot. With the exoskeleton is a periodic phenomenon, and a complete intention estimation of taking a step, discrete gait planner walking cycle is composed of two phases: a double-support obtains gait parameters such as step length S and step dura- phase and a single-support phase. The double-support phase tion T. DMPs are utilized to regenerate trajectories with begins with the heel of the forward foot touching the ground these diﬀerent parameters S, T . Joints control serve these and ends with the toe of the rear foot leaving the ground. trajectories to lead exoskeleton and patient move forward. During the double-support phase, both feet are in contact During the process of taking a step, online gait regulator with the ground. During the single-support phase, one foot adjusts the parameters S, T based on gait planer to coun- is stationary on the ground and the other foot swings from teract disturbance. the rear to the front. After the end of a step (swing leg 3.2. Model of Human and Exoskeleton. In many applications touches the ground), human-exoskeleton system enter dou- of exoskeletons, patients walk with crutches to keep balance [8, ble support phase. 9, 11, 12]. Thus, quadruped robot model is utilized to express In this phase, the patient has two choices: stopping to these human-exoskeleton system. With this model, static sta- walk and taking a new step. As shown in the left side of ble based on CoM is considered during the walking process. Figure 3, the patient moves forward/backward slightly; weight will load on front/behind leg. Thus, we can also use Although patients are enabled to walk again with this approach, for stability, they must rely on crutches, and their LIP to model this system. With this model, we can design a intention estimator for take a step according to the concept gait pattern is less ﬂuent and slower than natural gait. Thus, for achieving fast and natural gait, we use LIP in sagittal plane of orbital energy diagram. The orbital energy E [24] can be obtained with the inte- to model the human-exoskeleton system as Figure 2. Linear gration of x x − g/z x =0: inverted pendulum (LIP) is widely used in biped robot [18, 22, 23]. In LIP, we model the body with a point mass with posi- g 1 g 2 2 tion r at the end of a telescoping mechanism (representing the xx − xxdt = x − x = E 4 z 2 2z leg), which is in contact with the ﬂat ground. The point mass is kept on a horizontal plane by suitable generalized forces in the It is the sum of two terms: dynamic energy and potential mechanism. Most exoskeletons’ ankle joints are not actuated energy. It is conserved during a single support phase. Given and activated [8–10]. Hence, the base of the pendulum can E =0, LIP moves to straight up position with x =0. We can be seen as a point foot, with position r ankle. Foot position infer that if initial x >0, LIP can move over the straight up changes, which occur when a step is taken, are assumed instan- position with E >0, otherwise it will move back. Thus, letting taneous and have no instantaneous eﬀect on the position and E =0, we can obtain a line: x =± g/zx. With axis x, x and velocity of the point mass. Patients can apply external this line. As shown in Figure 3, we separate the motion states force to CoM with crutches to interact with exoskeleton. of LIP x, x, E into 8 regions. Thus, we call it orbital diagram. By deﬁnition mentioned before, we can obtain motion When x <0 we can get results from orbital diagram: equation of point mass (external force set to 0) as follows: (1) If E >0, x <0 and x >0, LIP would cross the straight r θ +2rrθ − grsin θ = , up position. 2 f (2) If E <0, x <0 and x >0, LIP would move back to r − rθ + gcos θ = , M initial position. 4 Applied Bionics and Biomechanics Dynamic balance gait approach Human Trigger a step (S, T) Trajectories generator Sensor data Discrete gait planner Intention Estimater by DMPs Exoskeleton sensor data Online gait regular Trajectories in Cartesian space Joint torque Trajectories in joint space Inverse kinematic PID joint controllers Figure 1: The framework of dynamic balance gait planning. min-jert method is used to model this trajectory. However, with these approaches, the whole trajectory must be replanned if a single point of motion changed. In our approach, we f f cos (휃) obtain the foot trajectory from normal person and regenerate it with targeting step length S and duration T. DMP is utilized to regenerate this trajectory to adjust this trajectory online. f sin (휃) DMP has been widely employed in robotic applications, since it can solve ﬂexible modelling problems with coupled -Mg terms [28]. It is easy to learn with statistical methods and can be adapted through a few parameters after imitation learning [29, 30]. Moreover, it can quickly be adapted to the inevitable perturbations of a dynamically changing, stochastic environment. Modelling a trajectory with the framework of DMP, a trajectory x t is supposed to be Figure 2: Model of exoskeleton and human based on LIP. the output of a mass spring damper system perturbed by a force term: (3) If E <0, x <0 and x <0, LIP would move backward. τv =Kg − x − Dv + g − x f , (4) If E >0, x <0 and x <0, LIP would move backpack. τx = v, As shown in Figure 3, if stand leg is front leg and the state where x and v indicate the position and velocity of the sys- of system can be described with state 1, 7, and 8, then a step tem, respectively. x and g are the start and goal positions. must be taken forward to prevent falling down. Commonly, τ is a temporal scaling factor. K and D are the spring and after the transition of weight, system will come to state 1 damping factors of the system. Therefore, with a known x t , before 7 and 8. If stand leg is behind leg and the state of sys- f t can be calculated through the inverse of the system. Then, tem can be described in state 3, 4, and 5, exoskeleton must f can be learned by combining with Gaussian kernels: take a step backward for preventing falling. Thus, after deter- mining stand leg, we can obtain the intention of patient (step 〠 ω ψ s s i i i=1 forward or step backward) by the quadrant of orbital energy fs = , 6 〠 ψ s diagram, the status x, x, E belong to. i=1 where ψ = exp −h s − o are Gaussian basis functions 3.4. Gait Description with DMPs. As many studies on gait i i with center o and width h . w are weights which should be planning [25–27] have assumed that the double-support i i i learned. The phase variable in the nonlinear function (6) is phase is instantaneous, we focus the gait of single-support utilized to avoid f directly dependence oﬀ on time. Use phase. If foot trajectories and the hip trajectory are already ﬁrst-order dynamics to deﬁne the phase variable x: known, all joint trajectories of the exoskeleton can be deter- mined by kinematic equations. The walking pattern can τs = αs 7 therefore be denoted uniquely by foot trajectories and hip trajectories. As most of exoskeleton ankle joints are not actu- The goal g is close to the start position x , a small change ated, foot of stand leg can be modeled as point. With known 0 in g may lead to huge accelerations, which may reach the initial position and velocity of LIP, trajectories of hip are limitation of the exoskeleton system. Therefore, modiﬁed known. Thus, gait pattern can be modeled by trajectories of system equations introduced in [31] are used: ankle joint of swing leg. In [21], gait pattern is formulated by the constraints of a complete foot trajectory and generate τv =Kg − x − Dv +Kg − x s + Kf s , 8 the foot trajectory by third spline interpolation. In [10], Applied Bionics and Biomechanics 5 Z · X= −X Backward Forward E > 0 E > 0 E < 0 E < 0 E < 0 E < 0 Front leg Behind leg E > 0 E > 0 Z · X=− −X Figure 3: In double-support phase, state of human-exoskeleton system and orbital energy can be describe with the diagram with 8 quadrants. Trajectories Generated by DMPs where the third term can avoid jump movements at the 0.14 beginning of each step. After obtaining the target function: 0.12 τv + Dv 0.1 s = − g − x + g − x s, 9 target 0 0.08 0.06 the weighted parameters ω are able to learn via statistical learning methods. With speciﬁed start position x and goal 0.04 position g, the foot trajectories can be generated through 0.02 the learn weights ω . In our approach, we ﬁrst imitate trajec- tories of foot of swing leg in single-support phase x t , z t −0.15 −0.05 0.05 0.15 0.25 0.35 0.45 0.55 with a duration of 1 s. Then, as shown in Figure 4, we regen- X (m) erate trajectories with diﬀerent S, T by changing τ and g by following equations: Goal = 0.2 Goal = 0.5 Goal = 0.3 Goal = 0.6 g = S, Goal = 0.4 g =0, 10 Figure 4: DMPs of foot trajectories with diﬀerent parameters S, T τ = Tτ , new original swing leg leaving the ground and end with contacting the ground. T denotes the time cost in this process called gait where τ is the time constant of DMP learned before. original duration. In the ﬁrst step, if no external force posed on LIP, we can obtain the x t and x t and the E with ini- 3.5. Discrete Gait Planner. Aiming to obtain balance gait, we 1 1 1 tial the x 0 and x 0 . At the moment of leg switching, deﬁne the concept of balance based on N-step capturability 1 1 velocity of CoM does not change (x T = x 0 ) [22, 23]. [18, 32]: the ability of a legged system to come to a stop with- 1 2 Thus, we obtain orbital energy of second step as the follow- out falling by taking N or fewer steps. As exoskeleton mod- ing equation: eled by LIP, “stop” means orbital energy is 0 (x =0 when x =0). Thus, the balance of exoskeleton is deﬁned as: the 1 g orbital energy can be controlled to 0 with the limitation of x T − S − x T = E , 11 1 1 2 swing speed and length of leg. In other words, as shown in 2 2z Figure 5(a), if E is too large to decrease even extending swing leg with max speed, CoM of LIP will go to the limitation of where S is step length shown in Figure 5(b). With this equa- stand leg and body rotate around the tip of toe as shown. tion, orbital energy of second step can be controlled by However, walking with exoskeleton, patients can change adjusting S, T . orbital energy by applying external force with crutches. Given the aiming orbital energy E , the gait planer Thus, for walking easily, they expect to walk several steps obtains S, T at each beginning of step. This planner is called continuously and smoothly without applying much force discrete gait planner (DGP), since it plans the gait at the on exoskeleton. Therefore orbital energy needs to keep at a beginning of each step. positive value. As the x t and x t is the nonlinear function of t,we 1 1 To control orbital energy, we consider two steps as shown cannot solve it directly. Moreover, for a given targeting E , in Figure 5 and consider that the walking gait begins with the mount of solutions is inﬁnite. As we learn the trajectory Z (m) 6 Applied Bionics and Biomechanics { 1 }{ 2 } 1· E = − x , x = 0 Stand leg Stand leg Foot switch moment Swing leg Swing leg Single support state Trajectory of swing foot (a) When orbital energy is too large to decrease, LIP model falls down (b) Control orbital energy by changing step length S Figure 5: Deﬁnition of balance with orbital energy. 12 3 4 56 7 8 Figure 6: Snapshot of simulation during walking. ̂ ̂ (S, T) recorded from healthy person, we expect that the tra- 3.6. Continuous Gait Regulator. As we mentioned, DGP plans jectory regenerated by our approach is similar to the original a gait at beginning of the step and adjust the orbital energy of one. Thus, we formulate this problem as optimization prob- the next step. After gait planning, trajectory of foot is ﬁxed lem as follows. during a step. While, if a disturbance occurs during single- support phase, the gait cannot change until leg switching 2 2 2 ̂ ̂ ̂ argmin JS, T = α E −ET + β S − S + γ T − T moment. Thus, we design a continuous gait regulator S,T (CGR) to adjust the gait continuously during swing phase. CGR adjusts gait by changing the parameters S, T s t : < v , S < S , T > T , max max min obtained from discrete gait planner. It improve the DGP’s ability of keeping balance. In each sample time i, we can obtain the x i and x i . We calculate S , T with the same i i ̂ ̂ ̂ optimal approach of DGP and update remain time T where E, S, and T are target values of orbital energy, step remain of original trajectory generated by DGP. Then, we change length, and duration of gait. α, β, and γ are weighted param- the parameter of the DMPs with g = S and τ = T /T . eters. Gradient descent method is utilized to solve this opti- i remain i mization problem with gradient as follows: 4. Experiments on Simulation P = P − λ∇JS, T , 13 i i−1 In this section, we ﬁrst lay down on the performance metrics deﬁnition and evaluate this approach in simulation platform. where P = S , T and ∇J s, t is shown as follows: i i i 4.1. Performance Metrics Deﬁnition. Evaluating the perfor- ∂J 2αg 2β S − S + ET − E xT − S mance of proposed approach is to evaluate the ability of ∂S keeping balance especially when a disturbance occurs. As xg ∂J we mentioned before, balance of system is depended on the ̂ ̂ 2α ET − E x +1 + γ T − T z controllable ability of orbital energy. Thus, in our evaluation, ∂T we exert disturbance and compare orbital energy of diﬀerent approaches during the whole process. Iterations of optimization ends with ∇J S, T =0 or numbers of iterations reach the limitation. If ∇J S, T is to 4.2. Simulator Introduction. We build a simulator to evaluate 0 after iterations, we obtain the solution S, T closer to the the performance of our approach in a desktop-computing targeting E at this step. And E will be more closer to target platform with CPU:i7 4790 k and 8 G RAM with Gazebo E step by step. robotics simulation software as shown in Figure 6. As the Applied Bionics and Biomechanics 7 0.24 0.8 0.19 0.6 0.4 0.14 0.2 0.09 −0.2 0.04 −0.4 −0.01 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ms) X (m) DGP Fixed gait: S = 0.35 m T = 0.25 s DGP Fixed gait: S = 0.35 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s (a) Orbital energy of diﬀerent gait patterns with external force 5 N (b) Foot trajectories of diﬀerent gait patterns with external force 5 N 0.24 0.8 0.19 0.6 0.14 0.4 0.2 0.09 −0.2 0.04 −0.4 −0.01 0 0.5 1 1.5 2 2.5 3 3.5 4 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 X (m) Time (ms) DGP Fixed gait: S = 0.35 m T = 0.25 s DGP Fixed gait: S = 0.35 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s (c) Orbital energy of diﬀerent gait patterns with external force 15 N (d) Foot trajectories of diﬀerent gait patterns with external force 15 N 0.24 0.8 0.19 0.6 0.4 0.14 0.2 0.09 −0.2 0.04 −0.4 −0.01 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ms) X (m) DGP Fixed gait: S = 0.35 m T = 0.25 s DGP Fixed gait: S = 0.35 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s (e) Orbital energy of diﬀerent gait patterns with external force 25 N (f) Foot trajectories of diﬀerent gait patterns with external force 25 N Figure 7: Experimental results of diﬀerent gait patterns with external force (5 N, 15 N, 25 N). patient holds crutches to preserve falling sideways during exoskeletons. PID controllers with 1000 Hz sample frequency normal walking, we model this coupled system as model are used in each joint with limitation of output torque shown in Figure 6 and constrain the motion in sagittal plane. 200 N.M. At each joint, joint encoders are embedded to obtain motion state of joints. We simulate 3000 ms in each trail with In this model, hip joint (ﬂexion/extension) and knee joint (ﬂexion/extension) are actuated just like most of initial state of LIP: x =0 1m, x =0 1 m/s, z =0 7m.The init init Orbital energy (J) Orbital energy (J) Orbital energy (J) Z (m) Z (m) Z (m) 8 Applied Bionics and Biomechanics 0.24 0.8 0.19 0.6 0.4 0.14 0.2 0.09 −0.2 0.04 −0.4 −0.01 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ms) X (m) DGP Fixed gait: S = 0.35 m T = 0.25 s DGP Fixed gait: S = 0.35 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s (a) Orbital energy of diﬀerent gait patterns with external force −5N (b) Foot trajectories of diﬀerent gait patterns with external force −5N 0.24 0.8 0.19 0.6 0.4 0.14 0.2 0.09 −0.2 0.04 −0.4 −0.01 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ms) X (m) DGP Fixed gait: S = 0.35 m T = 0.25 s DGP Fixed gait: S = 0.35 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s (c) Orbital energy of diﬀerent gait patterns with external force −15 N (d) Foot trajectories of diﬀerent gait patterns with external force −15 N 0.24 0.8 0.19 0.6 0.4 0.14 0.2 0.09 −0.2 0.04 −0.4 −0.01 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ms) X (m) DGP Fixed gait: S = 0.35 m T = 0.25 s DGP Fixed gait: S = 0.35 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s DGP and CGR Fixed gait: S = 0.3 m T = 0.25 s (e) Orbital energy of diﬀerent gait patterns with external force −25 N (f) Foot trajectories of diﬀerent gait patterns with external force −25 N Figure 8: Experimental results of diﬀerent gait patterns with external force (−5N, −15 N, and −25 N). targeting orbital energy is set to be 0 4J.Fourgaitpatternsare Diﬀerent disturbance: −5N, −15 N, −25 N, 5 N, 15 N, compared in our experiment: and 25 N in sagittal plane is posed on LIP from 500 ms Gait with ﬁxed parameters: S =0 35, T =0 25 . to 2000 ms. A trail ends if the model falls down during Gait with ﬁxed parameters: S =0 3, T =0 25 . walking. Orbital energy and foot transition of diﬀerent Gait generated by DGP. gait patterns are recorded for evaluating the ability to Gait generated by DGP combined with CGR. keep balance. Orbital energy (J) Orbital energy (J) Orbital energy (J) Z (m) Z (m) Z (m) Applied Bionics and Biomechanics 9 4.3. Experiment Results. Figure 7 illustrates the simulation Conflicts of Interest results of diﬀerent gait patterns with positive external force The authors declare that there is no conﬂict of interests as disturbance: 5 N, 15 N, and 25 N. With ﬁxed gait pattern, regarding the publication of this paper. the model of human-exoskeleton in simulation falls down forward after 5 steps. Patients have to control body with stick to keep balance with ﬁxed gait. Both DGP and DGP combin- Acknowledgments ing with CGR can keep balance with disturbance from 5 N to 15 N. As disturbance increases, the error orbital energy of This research was supported by the National Natural Science Foundation of China (no. 61503060, 6157021026). This DGP increases signiﬁcantly. With DGP alone, orbital energy of system cannot get back to given target after step taking. research was supported by the Fundamental Research Funds for the Central Universities (ZYGX2014Z009). As shown in Figure 7(f), trajectory of swing foot trajectory generated by DGP combined with CGR adjusts the step length after encountering a disturbance. Thus, DGP com- References bined with CGR achieves better performance than DGP in orbital energy control. [1] World Health Organization, Spinal Cord Injury, July 2017, Simulation results with native external force as distur- http://www.who.int/mediacentre/factsheets/fs384/en/. bance is shown in Figure 8. Walking with ﬁxed gait model, [2] R. W. Teasell, J. T. Hsieh, J. A. Aubut, J. J. Eng, A. 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