Adaptive Switching Control Based on Dynamic Zero-Moment Point for Versatile Hip Exoskeleton Under Hybrid Locomotion

In this article, an adaptive switching controller based on the dynamic zero-moment point for versatile hip exoskeleton is proposed. The linear finite hysteretic state machine is designed to recognize hybrid motion phases. The torque planning strategy based on dynamic zero-moment point is deployed to obtain assistant torque adaptively under different locomotion. Experiments are carried out to verify the performance of the controller, confirming the stability and accuracy of the motion phase recognition, which also demonstrates excellent kinematic performance. The net metabolic rate can be reduced by 6.93% while wearing the versatile hip exoskeleton walking. The integrated surface electromyography can be reduced by 54.8% while wearing the exoskeleton lifting objects. Compared with existing research, the performance of the proposed controller has significant advantages. The proposed controller is capable of multiple types of locomotion, including flat walking, stair climbing, and lifting heavy objects with low complexity and energy consumption.

back symptoms [1]. Exoskeletons are increasingly adopted to assist human mobility and avoid injury. Such equipment provides increased strength and endurance to the wearer and reduces their metabolic rate. The versatile hip exoskeleton is a typical type of versatile lower limb exoskeleton that can enhance the capability of wearers in both cyclical locomotion (walking, running, upstairs, downstairs, etc.) and acyclic locomotion (sitting down, standing up, lifting, squatting, etc.) [2]. Numerous hip exoskeleton prototypes have been presented and refined [3].
Generally speaking, the controller of a versatile exoskeleton consists of four parts: locomotion mode recognition (LMR) algorithm, motion phase recognition (MPR) algorithm, torque planning strategy, and basic control law [4], [5], [6]. The LMR algorithm is used to recognize the locomotion of the wearer such as walking, sitting, climbing stairs, etc. The MPR algorithm recognizes the motion phase, such as the gait phase, to provide triggers to the controller. The torque planning strategy ensures the stability of the human body while obtaining desired assistance torque. The basic control law ensures the accuracy of torque provided by actuators.
The LMR algorithm is mostly implemented by data-driven methods. Both deep learning methods and machine learning methods are feasible in the LMR topic. Deep learning methods have significant accuracy, while high-performance computing platforms are required [7]. Machine learning methods can be deployed on mini-type devices with lower consumption while ensuring the availability of precision [5], [8], [9]. LMR algorithms can recognize the locomotion mode to reconstruct the MPR algorithm and the control strategy.
The torque planning strategy can be designed based on the dynamic model. The springy leg force generation and partial interactive foot force feed forwarding were deployed as torque planning strategies on the HUMA (a lower limb exoskeleton prototype) [14]. The exoskeleton developed by the Samsung Advanced Institute of Technology calculated desired assistance torque by gait phase [15]. Yong et al. [16] proposed repetitive learning control based on the dynamic rigid model to design assistant torque. Zero-moment point (ZMP) model-based methods have been widely used to generate the trajectory of movement during the stance phase [17], [18], [19]. These ZMP-based methods can maintain the stability of the lower limb exoskeleton robot during walking, climbing, turning, etc., and have the advantage of adapting to hybrid locomotion.
The basic control law has been extensively studied by researchers compared with the previous three parts. Liang [20] found that a modified proportional-integral-derivative controller could follow human movements successfully by providing power assistance, while direct torque control was deployed in an exoskeleton presented by Seo et al. [15].
For each type of locomotion, the MPR algorithm and the torque planning strategy need to be designed specifically in most cases. The full control architecture of a versatile hip exoskeleton under hybrid locomotion usually consists of an LMR algorithm with multiple groups of MPR algorithms and torque planning strategies based on the target task. Sano et al. [4] implemented one LMR algorithm, two MPR algorithms, and three torque planning strategies in the control architecture for a versatile hip exoskeleton. Furthermore, control architecture with one LMR algorithm, two MPR algorithms, and two torque planning strategies is deployed by Parri et al. [5] for a versatile hip exoskeleton.
As the exoskeleton becomes more versatile today, so will the range of locomotion types. Then, the control architecture of exoskeletons will also become more complex. The complexity of control architectures will lead to higher hardware requirements and higher energy consumption. Moreover, the diversity of algorithm switching may also lead to unpredictable instability. Therefore, more concise control architectures were developed by researchers [6], [21]. Wei et al. [6] proposed a concise control architecture based on a finite-state machine as an LMR-MPR algorithm, which is adaptive to lifting and walking. Although the control architecture of the versatile exoskeleton was simplified, manual design is required for plenty of empirical transition conditions, which caused intense uncertainty and imperfect performance. A more concise and theoretical approach is required.
Motivated by the above analysis, the major contributions of this article are as follows.  54.8% while lifting an object indicating multilocomotion capability. Moreover, experimental verification was demonstrated on the prototype hip exoskeleton. The precision rate of LFHSM, the kinematic performance of control architecture, and the physiological performance of the prototype exoskeleton are thus verified. These experimental results illustrate the advantages of the proposed control method. Besides, the LMR-MPR algorithm and the DZMP torque planning strategy are both extensible in terms of locomotion.
The rest of this article is organized as follows. The proposed versatile hip exoskeleton is outlined in Section II, and the adaptive switching control is presented in Section III. The experimental results with detailed analysis are given in Section IV. Finally, Section V concludes this article.

II. MECHATRONICAL DESIGN OF THE VERSATILE HIP EXOSKELETON
The overview of the versatile hip exoskeleton is provided in Fig. 1. The versatile hip exoskeleton can provide support to the subject by unloading the spine when performing lifting movements and providing torque assistance when performing walking or climbing movements.
The design of the mechanical system and the electronic system of the versatile hip exoskeleton is demonstrated in Fig. 2. The design of the mechanical system shows that there are four degrees of freedom (DoF) (two active DoFs and two passive DoFs) in the proposed exoskeleton. The design of the electronic system is also demonstrated. Two nine-DoF inertial measurement units (IMUs) on the thighs are deployed to measure the motion of the wearer.
The main controller consists of an STM32F407VET6 and a keyboard used to adjust the output gain and the preinput slope of the controller. The selected microcontroller (STM32F407VET6) has the advantages of a multisignal interface and low energy consumption, which is suitable for exoskeletons. The two controller area network interfaces isolate the sensor bus from the actuator bus, as shown in Fig. 2, thereby reducing the busload and improving the communication efficiency. Besides, the advantages of low power consumption and low heat are applicable to field equipment such as exoskeletons. For each hip, there is a brushless dc motor providing torque assistance. Parameters of the motor were selected based on the method presented by Calanca et al. [22], which is shown in Fig. 2. The primary mission of the proposed hip exoskeleton is to assist the wearer in carrying heavy objects. In Fig. 2, the blue points represent the task required performance of the exoskeleton. The requirement of the mission was measured by a Vicon optical motion capture system. The green points in Fig. 2 show the parameter requirements of motors based on the target mission. The red points demonstrate the parameters of the selected motors for the hip exoskeleton. The parameters of the selected motors completely cover the demand parameters of the motor with redundancy. The motors have built-in rotational encoders in motors to monitor the angle and angular velocity. The drivers of the motors work in torque servo mode. Based on the load simulator test, the static torque error of the motors is less than 5%, and the dynamic torque error is less than 8.5%.

III. ADAPTIVE SWITCHING CONTROL BASED ON THE DZMP
The architecture of the adaptive switching controller is shown in Fig. 3. The controller can be mainly divided into two parts: the LMR-MPR algorithm and the torque planning strategy. The LFHSM is deployed as the LMR-MPR algorithm. The torque planning strategy is alterable based on the state of the LFHSM.
The DZMP strategy is deployed as the assistive strategy, while the basic servo strategy is deployed as the transparency strategy.

A. LMR-MPR Algorithm Based on the LFHSM
The primary mission of the hip exoskeleton is transportation, which can be divided into three types of locomotion (flat ground walking, upstairs climbing, and heavy object lifting), as shown in Fig. 4. Each locomotion has a unique motion phase that requires assistance from the hip exoskeleton. As such, these three locomotion can be transformed into four states for the LFHSM. The system state can be described as s ∈ {DT, LT, RT, DH}. The DT, LT , and RT are the states the DZMP strategy deployed for the dual, left, or right hip. The DH is the state that the basic servo strategy is deployed for dual hips.
The state transition diagram is shown in the LMR-MPR algorithm zone of Fig. 3. Thus, the state transition conditions can be designed as a linear plane. Kinematics data measured by IMUs can be described as x = [ θ l θ r q l q r ], where θ l and θ r are the angles of the left hip and the right hip, and q l and q r are the angular velocities of the left hip and the right hip, respectively. Hence, the definition of state transition plane can be given as δ where a s 1 →s 2 = −a s 2 →s 1 and b s 1 →s 2 = −b s 2 →s 1 . a s 1 →s 2 and b s 1 →s 2 are parameters of state transition condition learnt from data. Hence, δ s 1 →s 2 = −δ s 2 →s 1 . The linear structure can reduce the time complexity of recognition. The learning algorithm is given in the next subsection.
To improve the robustness of the system, the condition of state transition with hysteresis characteristics is designed. The main function of hysteresis characteristics is to reduce the false positive rate of stance phase recognition to ensure the safety of the wearer. Besides, the hysteresis characteristics also have a low-latency antijitter function. The state transition condition with hysteresis characteristics can be modified as where σ s 1 →s 2 is the hysteresis parameter. Besides, σ s 1 →s 2 = σ s 2 →s 1 is the half distance between transition conditions π s 1 →s 2 and π s 2 →s 1 . The spaced parallelism of transition conditions of two mirrored states transitions brings in the hysteretic characteristic of the system.

1) Training the LFHSM With Motion Data:
For the state transition process of s 1 → s 2 , in order to obtain a reliable state switching condition, the parameters of switching condition that need training are {a s 1 →s 2 , b s 1 →s 2 , σ s 1 →s 2 }.
The training database is provided by the Beijing Institute of Mechanical Equipment. The locomotion and motion phases are labeled, while the angle and angular velocity of each joint are provided by the database. For certain states, s 1 and s 2 , the sampled human motion data can be described as where N is the number of sample points. The labeled system state can then be recorded as   N]). In addition, the desired classification result can be expressed as The learning algorithm is designed based on optimization methods. The basic target of the training algorithm is to ensure the accuracy of classification between s 1 and s 2 , which can be described as Besides, the hysteretic characteristics should not affect the classification accuracy of the LFHSM, which indicates that σ s 1 →s 2 should satisfy Then, the hysteretic parameter σ s 1 →s 2 can be written as where ξ ∈ R and ξ = 0. The second target is to improve the robustness of the algorithm. Therefore, the hysteretic characteristics of the LFHSM should be as obvious as possible. Thus, σ s 1 →s 2 should be maximized, while accuracy is guaranteed. Therefore, the optimization target can be described as max a s 1 →s 2 ,b s 1 →s 2 σ s 1 →s 2 .
As the optimization target is settled, it is then further simplified. First, (7) leads to Then, the scaling conditions of convergence are considered where x j is the nearest point to the plane. The optimization problem can then be re-expressed as subject to Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. The optimization problem described in (11) and (12) is a minimal convex quadratic programming problem that can be solved by the classic sequential minimal optimization algorithm.

2) Arbitration Strategy of the LFHSM:
The multitarget state transition decision is required under continuous hybrid locomotion. A decision binary tree is designed to solve the arbitration strategy problem, which is shown in Fig. 5. The root node of each decision binary tree indicates the current state. The leaf nodes of each decision binary tree indicate a transition target state. For target states of equal priority, (1) is deployed as the decision conditions with no hysteresis characteristics. For target states with priority, (2) is deployed as the decision conditions with hysteresis characteristics. The priority of each state is represented by the depth of the decision point in the binary tree.

B. DZMP Torque Planning Strategy
The DZMP strategy is an assistive strategy deployed for the stance leg. In the DZMP strategy, the desired torque of motors is obtained by an analysis of human body dynamics based on the DZMP model. Human movement in different locomotion is abstracted as movements of DZMP and the center of mass (CoM). As the hip exoskeleton has no active DoF in the lateral direction, only the xz coordinate system is considered. A sketch of the human walking process is shown in Fig. 6. The CoM coordinates are defined as X m = {x m , z m }, θ is the angle of the hip joint of the stance leg, φ is the angle of the knee joint of the stance leg, l t is the thigh length, l s is the shank length, and θ is the angle of the hip joint of the swing leg. The DZMP coordinates are defined as X p = {x p , z p }. In addition,• means the velocity of •, while• represents the acceleration of •. Moreover, • d means the desired value of •, where • is a replaceable virtual  symbol. The knee angle is not acquirable and is assumed to be approximately fixed for the proposed exoskeleton. Hence, φ = 0 andφ = 0.
The basic formula of the DZMP strategy is shown as Hence, the acquisition of the movement intention of hip joints is vital in the controller design. First, the DZMP under different locomotion can be obtained. Various DZMP trajectories under different locomotion are illustrated in Fig. 7.
While climbing, the state of the LFHSM is LT or RT with the slope value provided by the user; the DZMP can be estimated as where K l is an empirical leg pose estimation coefficient meeting 0.5 < K l < 1.0. A slope is the slope angle of the terrain given by the user. While walking, the state of the LFHSM is LT or RT ; (14) can be simplified as While lifting, the state of LFHSM is DT ; the DZMP can be estimated as The estimation of the DZMP can be finally described as where F (θ, state) can be (14), (15), or (16) based on the state of the LFHSM. Second, the movement of the CoM can be obtained. The relationship between the joints angle and the CoM can be described as X m = l t sin(θ)) l s + l t cos(θ)) (18) andẊ m = l t cos(θ)) −l t sin(θ)) θ .
Third, the movement intention of hip joints can be obtained by the movement of the DZMP and the CoM. Based on the definition of the ZMP, the zero-moment condition of the DZMP can be expressed as where G 1 (X m , X p ) is a simplified notation to the first constraint ofẍ m .
To follow the human motion intention, which means maintain the velocity of the CoM partly, the supporting leg is subject to the following constraints:Ẍ Based on constraints (23) and (21), the predictive acceleration of the CoM can be obtained as Based on (19), it can be given thaẗ WhileẌ m is acquirable by (24), then where α 1 and α 2 are selected parameters subject to α 2 1 +α 2 2 =1. Therefore, based on the appropriate abstraction of human movement, the motion intention of the hip angle under different locomotion can be obtained.

C. Basic Servo Strategy Based on Direct Torque Planning
The basic servo strategy is a transparency strategy deployed for the swing leg. The model of the swing part of the hip exoskeleton can be described as a free pendulum where J is the moment of inertia of the one side leg, m is the mass, g is the acceleration of gravity, and M h is the torque provided by the hip motor.
The basic servo strategy is then designed by the direct feedback torque control method. The desired motor torque can be obtained as

IV. EXPERIMENTAL VERIFICATION
Three experiments were designed to verify the effectiveness of the proposed adaptive switching controller. The hybrid motion experiments were designed to verify the accuracy of the LMR-MPR algorithm and the validity of the switching strategy. The NMR experiments and sEMG experiments were then employed to verify the effectiveness of the hip exoskeleton with the designed controller. The experiments were performed at the Beijing Institute of Mechanical Equipment (Beijing, China).

1) Experiment Protocol:
Ten healthy subjects (eight males and two female) (average height: 1.71 ± 0.14 m; average weight: 65.4 ± 22.1 kg) volunteered to participate in the experiment. A track was defined by Table I, including all the investigated locomotion. Each subject underwent the following two sessions. 1) They performed the track twice wearing the exoskeleton with the adaptive switching controller. 2) They performed the track twice wearing the exoskeleton with the adaptive switching controller without hysteretic character. (The linear finite-state machine (LFSM) is deployed as LMR-MPR algorithm.) 2) Verification of the LFHSM: The accuracy and real-time performance of the LFHSM are verified by the hybrid motion experiment. Fig. 8 shows the confusion matrix of the LMR-MPR algorithm based on the LFHSM and the LFSM (LFHSM without hysteretic character). The proportions, the precision rate, the recall rate of each state, and the accuracy of the algorithm are given in the matrix. As shown in Fig. 8(a), the accuracy and stability of the LMR-MPR algorithm are largely guaranteed. Besides, the LFHSM can ensure the balance and safety of the exoskeleton. The precision rate of LT, RT, and DT is 99.8%, 99.7%, and 99.7%, respectively. The recall rate of DH is 99.3%.
The hysteretic characteristics have a significant effect on the exoskeleton based on the comparison between Fig. 8(a) and (b).  The accuracy of the LFHSM is 2.4% slightly higher than that of the LFSM. At the same time, the accuracy rate for states LT and RT increases by 7.6% on average, and the recall rate for DH increases by 7.3%.
The average absolute time error of the LFHSM is demonstrated in Table II. The average time error of recognition under level walking is 9.1 ms, which is extremely low. The average time error under hybrid walking (level walking, upstairs climbing, downstairs walking, uphill climbing, and downhill walking) is 14.3 ms. The average time error of lifting and squatting is 53.9 ms. The overall time error of the LFHSM is 16.2 ms.

3) Verification of the DZMP Torque Planning Strategy:
The performance of the torque planning strategy was quantified by analyzing the hip angle, the theoretical DZMP hip angle trajectory, the angle of the motors, and the torque command of the motors. Fig. 9 shows the motion data of a subject wearing the versatile hip exoskeleton under different locomotion (walking, climbing, and lifting). On the upside of each figure is a comparison of the exoskeleton hip angle with the human hip angle. On the downside are detailed curves of the motion phase and torque command generated by the DZMP strategy. The baseline torque represents the torque required to allow the exoskeleton to follow the movement of the wearer. The controller shows excellent performance. The hip joint curves of the subject and the exoskeleton are consistent, and the motion phases can be correctly recognized. During the DZMP strategy motion phase, the torque command of the motor is generated by the DZMP strategy in time maintaining the balance of the wearer.
Two gait cycles, while the subject is walking, is shown in Fig. 9(a). The assistance torque is generated properly and smoothly. Motion data of a subject climbing the stairs while wearing the hip exoskeleton are shown in Fig. 9(b). Comparing Fig. 9(a) and (b), the theoretical DZMP hip angle trajectory while climbing is also more drastic than that while walking. Energy output is higher than walking. Motion data of a subject lifting a heavy object while wearing the hip exoskeleton are shown in Fig. 9(c). In the phase of lifting, the torque command increases significantly. At the end of the movement, the torque command ensures the balance of the body and avoids waist hyperextension.
The performance of the DZMP strategy of the versatile hip exoskeleton under different locomotion is shown in Fig. 10. Fast walking requires more assistance torque than slow walking. At the same time, the assistance torque required to climb upstairs is greater. It can be concluded that the assistance torque generated by the DZMP strategy is consistent with the dynamic characteristics of the human movement. Based on Fig. 10(d), while walking downstairs, the command torque is similar to the baseline torque, and the exoskeleton provides little assistance to the body. As shown in Fig. 10(e), when the locomotion transits from walking to climbing upstairs, the gait stability is weak and the movement curve has a significant standard deviation. However, the DZMP strategy can still provide reliable torque assistance. These results show that the proposed DZMP torque strategy has a significantly robust multilocomotion performance. 1) They walked with a slope of 0°, with the exoskeleton.

B. NMR Experiments
2) They climbed with a slope of 15°, with the exoskeleton.
3) They walked with a slope of 0°, with no exoskeleton. 4) They climbed with a slope of 15°, with no exoskeleton. The interval time between each session is at least 4 h. The value of net metabolic rate was calculated based on the weight of the subject, the mass of carbon dioxide exhaled obtained by COSMED K5, and the duration of the experiment.

2) Verification of Assistance Efficacy While Walking:
The comparison of net metabolic rate between wearing the exoskeleton and not wearing the exoskeleton is shown in Fig. 11(a). Wearing an exoskeleton during climbing is shown to reduce the metabolic rate by 5.75% (p < 0.05), and wearing an exoskeleton while walking is shown to reduce the metabolic rate by 6.93% (p < 0.05). It can be concluded that the exoskeleton can significantly improve the efficiency of assistance while walking.

1) Experiment Protocol:
Four healthy subjects (four males) (average height: 1.77 ± 0.05 m; averaged weight: 70.6 ± 17.1 kg) volunteered to participate in the experiments. Each subject lifts a 20-kg object (standing upright, reaching for an object lying on the ground, grasping and lifting it, and reaching upright posture) wearing the exoskeleton twice and   without the exoskeleton twice. To collect muscular activity data, the wireless sEMG measurement instrument (Noraxon Desktop DTS-8, USA) was deployed. According to the recommendations of SENIAM [23], the sEMG electrodes were placed to measure the bilateral activation of the muscles responsible for lifting objects, namely the Erector Spinae Longissimus Lumborum (LL) and semitendinosus (ST).

2) Verification of Assistance Efficacy While Lifting
Object: The comparison of integrated sEMG of LL and ST between wearing the exoskeleton and not wearing the exoskeleton is shown in Fig. 11(b). The exoskeleton can significantly reduce the sEMG of LL by 54.84% (p < 0.05) while lifting an object. Besides, wearing an exoskeleton during lifting is shown to roughly reduce the sEMG of ST by 9.89% (p < 0.1). The results show that the exoskeleton can significantly improve the efficiency of assistance while lifting objects.

D. Discussion
Multiple groups of comparisons of this study and previous similar studies are presented. The comparison of accuracy and   Table III. Recent gait phase recognition algorithms that use IMUs as the major sensors and divide the movement into several motion phases [5], [24], [25], [26], [26], [27] were compared. The comparison of physiological performance (NMR and sEMG) of the exoskeleton prototype is shown in Table IV. Recent bilateral hip assistance exoskeletons [4], [28], [29], [30], [31], [32] were compared. The NMR is the indicator of assistance efficacy while walking. The integrated sEMG is the indicator of assistance efficacy while lifting objects.
As shown in Table III, the LFHSM has significantly lower time errors compared with other studies. The average walking time error of the LFHSM is 9.1 ms. The MPR accuracy of the LFHSM is also at the same level as that of the state-ofthe-art studies. The average lifting time error of the LFHSM is 53.9 ms. There are two main reasons for LFHSM's significantly low time error. First, the linear structure described in Fig. 5 ensures the extremely low time complexity of the algorithm. Second, the hysteresis design shown as (2) allows the algorithm to eliminate the procedure of recognition result antijitter, thus further improving the response speed. For lifting movement, the main reason for the mediocre accuracy of the LFHSM is that lifting and squatting are classified as the same motion phase in the state design, limiting the recognition accuracy. Table IV shows that the prototype versatile hip exoskeleton deploying the proposed adaptive switching control strategy has reached state-of-the-art performance on walking tasks and lifting tasks. In walking tasks, based on NMR measurement, the proposed controller can achieve similar performance to the latest studies. On the lifting task, the proposed controller can achieve better results than the previous research, reducing the LL muscle activity by 55%. These results indicate that the DZMP torque strategy can generate appropriate assistance torque in both walking tasks and lifting tasks and has significant adaptability to hybrid locomotion. The DZMP torque strategy abstracting human movement under different locomotion into the movement of the DZMP and the CoM is effective.

V. CONCLUSION
In this article, a novel adaptive switching control architecture based on DZMP for versatile hip exoskeleton was proposed. Both cyclical and acyclic locomotion were available, while only one LMR-MPR algorithm and one torque planning strategy for assistance were implemented. An LMR-MPR algorithm for hybrid locomotion based on the LFHSM was proposed to obtain accurate MPR. The LFHSM had a significantly low time error (9.1 ms for walking and 53.9 ms for lifting) due to the novel linear hysteretic design. An adaptive torque planning strategy based on the DZMP was presented to obtain assistance torque under different locomotion. The exoskeleton deploying the DZMP strategy can reduce NMR by 6.93% while walking and reduce integrated sEMG by 54.8% while lifting an object indicating multilocomotion capability. In future studies, more types of locomotion will be considered by designing more states for the LFHSM and more DZMP estimation methods for the DZMP strategy based on the locomotion adaptability of the proposed control architecture.