## Abstract

With the rapid expansion of older adult populations around the world, mobility impairment is becoming an increasingly challenging issue. For the assistance of individuals with mobility impairments, there are two major types of tools in the current practice, including the passive (unpowered) walking aids (canes, walkers, rollators, etc.) and wheelchairs (powered and unpowered). Despite their extensive use, there are significant weaknesses that affect their effectiveness in daily use, especially when challenging uneven terrains are encountered. To address these issues, the authors developed a novel robotic platform intended for the assistance of mobility-challenged individuals. Unlike the existing assistive robots serving similar purposes, the proposed robot, namely, quadrupedal human-assistive robotic platform (Q-HARP), utilizes legged locomotion to provide an unprecedented potential to adapt to a wide variety of challenging terrains, many of which are common in people’s daily life (e.g., roadside curbs and the few steps leading to a front door). In this paper, the design of the robot is presented, including the overall structure of the robot and the design details of the actuated robotic leg joints. For the motion control of the robot, a joint trajectory generator is formulated, with the purpose of generating a stable walking gait to provide reliable support to its human user in the robot’s future application. The Q-HARP robot and its control system were experimentally tested, and the results demonstrated that the robot was able to provide a smooth gait during walking.

## 1 Introduction

Population aging is occurring all around the world. For example, in the United States, the number of older adults is expected to reach 71 million, accounting for 20% of the population, by 2030 [1]. As such, maintaining and improving the health and wellbeing of the large number of older adults is becoming an increasingly challenging task. Toward this goal, it is highly important for older adults to live an active lifestyle. Results from a large body of research highlight the role of regular physical exercise in the prevention of cardiovascular and neurodegenerative diseases [2,3] as well as the improvement of functional performances for elderly individuals [4,5]. Although the benefits of physical exercise are well known and well documented, a large number of elderly individuals are unable to maintain an actively lifestyle, with multiple causes including physical weaknesses and significant risk of injury resulting from falls [6].

Motivated by such challenges, various assistive devices have been developed to help elderly individuals and other mobility-impaired people. Existing devices available to the general public can be largely divided into two categories: mobility aids and wheelchairs. Mobility aids are simple mechanical devices that provide extra support to the users in locomotion, enhancing their balance control and reducing the load in their musculoskeletal structure in the lower limbs [7,8]. Although this type of device is inexpensive and easy to use, the operation of a mobility aid is completely manual (i.e., unpowered). During walking, a user has to lift and reposition the mobility aid with each gait cycle, causing extra physical and cognitive burden to the frail user [9]. Wheelchairs, in comparison, have a very different mode of operation. A wheelchair user is always seated, and thus the risk of fall is almost nonexistent. Further, powered wheelchairs enable users to move around with minimal energy consumption. On the other hand, when using a wheelchair, an individual has minimal lower-limb muscle activity and bone load bearing, which tends to accelerate the degeneration of the musculoskeletal systems [10].

In addition to the devices described above, new assistive devices have also been developed in recent years, leveraging the latest actuation, control, and computational technologies. A typical example is the functionally enhanced walkers, such as the PAMM (personal aid for mobility and monitoring), which monitors the user’s health through embedded sensing approaches such as ECG measurement [11]; the walking rehab aid, which assists and improves mobility through interaction force recognition [12]; and the PAM-AID (personal adaptive mobility aid), which has a capability of automatic steering for obstacle avoidance [1315]. The addition of such novel functions improves the user’s experience, but such wheeled devices still suffer from a common limitation in their adaptability to challenging environments. Specifically, people’s living environment is full of small obstacles, such as roadside curbs, small objects in walkways, and a few steps leading toward a building’s entrance. Such obstacles are easy to overcome for young healthy individuals, but could pose significant challenges to mobility-impaired individuals. Existing assistive devices have very limited efficacy in helping their users to overcome these obstacles, as they were developed primarily for level-ground use. Further, manipulating the assistive devices to avoid or overcome such obstacles may pose extra challenge, considering the low physical capabilities of the device users.

Such observation motivated the authors to develop a fundamentally different type of assistive device, with the goal of providing a substantially improved capability in overcoming the small obstacles ubiquitous in people’s daily life. The key innovation of this work in the use of legged locomotion, which provides superior environmental adaptability compared with wheeled locomotion [16]. Legged locomotion for mobile robots has been explored by numerous investigators, and the majority of related works are focused on quadrupedal robots (robots with four legs). For example, the Big Dog robot by Boston Dynamics demonstrated an excellent performance in overcoming difficult terrains such as slopes and rubble piles [17]; small-scale quadrupedal robots, such as AIBO [18] and Little Dog [19], have also been developed for purposes such as research and entertainment. Despite the large number of prior works on this topic, the use of quadrupedal robots for direct physical assistance to humans has not been attempted, to the best of the authors’ knowledge. As such, the research in this paper is unique in that it explores the quadrupedal locomotion as a novel mode of mobility for assistive devices. Under this general theme, the authors developed unique design and control approaches that facilitate the quadrupedal robot’s assistance to human users, which constitute the major contributions of this paper.

The assistive device presented in the paper, namely, quadrupedal human-assistive robotic platform (Q-HARP), is essentially a smart robotic walker configured as a quadrupedal robot. Each of the four legs has two powered robotic joints, providing sufficient mobility when accompanying and supporting the user in walking. As such, a mobility-impaired individual may enjoy a much higher level of mobility with this type of assistive devices in his/her daily living scenarios, as the aforementioned small obstacles no longer pose significant challenges. Based on the preliminary results presented in Ref. [20], this paper contains a thoroughly revised, more comprehensive description of the design, gait planning, control, and experimentation of the Q-HARP robot. Compared with Ref. [20], this paper illustrated the details of the gait planning processing, proposed a varying gait planning method to generate the gait trajectory in a discrete time domain, illustrated the real-time control system within a practical digital microcontroller system, proposed and illustrated an implementation of transitional gait planning based on the varying gait planning, and conducted a system-level experiment on the transitional gait beside a joint-level test to validate the feasibility and effectiveness of the present robotic platform.

The paper is organized as follows: Sec. 2 presents the design of the robot, including the overall structure of the robot as well as the designs of the robotic joints; Sec. 3 presents the gait planning algorithm; Sec. 4 presents the design of the real-time control system for the robot; Sec. 5 presents the planning algorithm for the transitional gait; Sec. 6 presents the experimental results; and Sec. 7 contains the conclusions of this paper.

## 2 Design of the Robotic Platform

As a brief overview of the research project, the Q-HARP is envisioned to be a special type of assistive robot that walks alongside the user and provides assistance and protection in the process, with or without physical contact from the user. The desired user interface will be constructed based on a novel 3D computer vision-based detection system, as demonstrated in a wheeled robot developed by the authors’ group [21,22]. To provide the desired mobility in accompanying the user and overcoming challenging terrains, a legged robotic platform was developed, with its design and control described in this paper. The robotic legs of the Q-HARP are expected to provide comparable performance as human legs, including the configuration, torque capacities, and kinematic performances. As shown in Fig. 1(a), the Q-HARP is supported by four identical robotic legs, in the configuration of knee joints bending inward and emulating two pairs of human bipedal legs to improve its compactness. Each robotic leg incorporates two powered rotational joints, emulating the functions of the hip and knee. An additional passive ankle joint with a flat foot is attached on each leg to provide support and angle compensation in the purpose of keeping a full flat ground contact. The details of the design of the hip and knee joints are introduced in the following part in this section.

As the robotic platform does not include a powered ankle joint for each leg (the ankle is the major source of power in human normal locomotion [23]), the hip on each leg is the major power source for the robot’s movement. Unlike the preliminary work conducted on a pneumatically actuated quadruped robot [24], the Q-HARP proposed in this paper is powered with direct current (DC) motor-based actuation approach which is compact and has greater potential of developing portable devices. However, the DC rotor actuation is typically characterized with high-speed and low-torque actuator, requiring a high-gear-ratio transmission to boost its torque and reduce the speed to power robotic joints for proper rotation. While, current such transmission systems tend to heavy, bulky and costly. As such, the primary design goal of the robotic joints is to maximize the torque capacity while still providing sufficient joint velocity within proper transmission. The hip joints here are designed to be driven by a novel two-stage miniature chain for velocity reduction and torque boosting. The knee joints are also powered by DC motor and driven through a transmission integrating belt and harmonic drive functions to boost the torque and maintain proper velocity. The prototype is as shown in Fig. 1(b). Considering the budget limit, two hip joints in the front side are currently powered with the harmonic actuators (FHA-17C-E, Harmonic Drive, Peabody, MA), which are expected to be replaced by the custom chain-driven hip actuators in the future. Based on the statistic principle of human legs in Ref. [25], each robotic leg has a thigh length of 0.394 m and a shank length of 0.343 m, and the ankle joint’s height with respect to the ground is 0.14 m. The top U-shape frame has a width of 0.46 m and a length of 0.91 m. The mass of the top frame is about 20 kg and uniformly distributed along the length of the frame. For the robotic legs, each thigh segment has a mass of approximately 2.7 kg, and each shank segment has a mass of approximately 1 kg. The masses of the thigh and shank mostly concentrate on the joints as lightweight hollow aluminum tubes are used to connect the joints.

Figure 2 shows the overall design of the hip joints. The components of the hip actuation system are all housed in the horizontal aluminum U-shaped frame. A high-current, low-speed DC motor (U8-10, T-Motor) is utilized to directly drive a 7-tooth small sprocket; then the small sprocket drives a 54-teeth sprocket supported by an intermediate shaft through a RS15 roller chain, forming the first stage chain drive. The intermediate shaft is attached with another 7-tooth small sprocket which drives a 45-tooth double sprocket through two parallel RS 25 roller chains, forming the second stage of chain. The two-stage design provides a total transmission ratio of 50:1, and thus the output joint torque reaches as high as 113 Nm calculated based on the DC motor properties. To tension the chains properly, the design in the Q-HARP incorporates a unique linear adjustment mechanism, as shown in Fig. 2(b). The intermediate shaft, which connects the output sprocket of the first stage and the input sprocket of the second stage, is placed on a slider that moves in the transverse direction. When the slider moves away from the center of the slide, the sprocket center-to-center distance increases for both stages so the chains will be tensioned simultaneously.

The knee joints in the proposed Q-HARP are originally powered prosthetic knees developed in the authors’ robotic prosthesis research [26]. For the completeness of presentation, the design of one of the knee joints will be depicted with simplicity here. As shown in Fig. 3, the knee is powered by an 8-pole brushless DC motor rated at 70 W (EC 45 flat, Maxon Motor). The motor essentially can generate a peak torque of 200 mNm for a short-term operation. A two-stage transmission is developed to provide a combined ratio of 150:1 to boost the torque and decrease its rotation velocity. The first stage is a timing belt drive with a ratio of 1.5:1; the second stage is a harmonic drive with a 100:1 gear ratio (SHD-20-100-2SH, Harmonic Drive, Peabody, MA). The purpose of selecting the harmonic drive is to utilize its large gear ratio reduction while maintaining a compact package. With the two-stage gear reduction, the output torque can reach as high as 30 Nm.

## 3 Gait Planning

Motion control of the Q-HARP robot is conducted with a bi-level control system: on the upper level, a gait planner plans the overall walking gait of the robot and generates the motion commands for all robotic legs and joints; on the lower level, a joint motion controller regulates the actuator output for each joint to obtain the desired joint motion. The upper-level gain planner is described in this section, and the joint motion controller will be described in Sec. 4.

Based on the Q-HARP’s desired functionality of walking assistance, maintaining the stability of the robotic frame in locomotion was given the top priority in research. According to such requirement, the gait for the Q-HARP locomotion was developed to be statically stable, with the center of mass (COM) always staying within the support polygon [27]. Although different from the dynamic characteristics of the human gait [28], such stable gait is expected to enable the Q-HARP to provide a stable support to the human user during the assistance.

The proposed method of gait planning adopts the framework of quadruped gait generator in Ref. [29], which ensures static stability while minimizing the cost of transport (COT). The process starts with the definition of the gait parameters: E is the leg stroke length, which is a distance that a foot is moved relative to the robot body during the stance phase of this leg; β is the duty factor of a leg, which is the fraction of the cycle when the leg is on the ground; λ is the stride length, which is the distance traveled by the COM during a total cycle [30]. The gait pattern used in this paper is a typical lateral sequence [31], in which the feet swing in the order of front left (FL), rear right (RR), front right (FR), and rear left (RL). Here we number the legs as FL (Leg 1), RL (leg 2), FR (Leg 3), and RR (Leg 4). These definitions are as shown in Fig. 4.

For the smoothness of the walking gait, it is desirable to maintain continuity in position, velocity, and acceleration of the planned path [32]. The method of polynomial spline interpolation [33] was selected for this purpose, leveraging its capability of providing smooth motion for robotic manipulators (e.g., Ref. [34]). When applying this method, we formulated the trajectories based on the unique kinematics of the quadrupedal robot, with the details provided below.

### 3.1 Planar Leg Trajectory.

Trajectory planning for a robotic leg was performed in an operation space, with the coordinate system defined as in Fig. 5. The following constraints are defined for the stance phase:
$x(t0)=E/2,x(t1)=−E/2x˙(t)=−v,y(t)=−hd$
(1)
where the origin is set at the center of the hip, x and y are the distances of the ankle joint to origin of the coordinate, hd is the desired height of the robot frame during walking, E is the stroke length, v is the desired walking velocity of the robot, and t0 and t1 are the initial and final time point of the stance phase, respectively.
The leg motion in the stance phase follows a linear trajectory with a constant velocity v and a fixed stroke length E. t0 is usually set as 0, and t1 = t0 + E/v. Based on such constraints, the linear trajectory can be expressed with the following equations:
$x(t)=E2−vty(t)=−hd$
(2)
The trajectory for the swing phase, from time t1 to tf, begins at the final position of the stance phase, lifts to a height hL (height of the foot to the ground) at t2, then ends at the initial position of the following swing phase to complete the cycle. The constraints are defined as follows:
$x(t1)=−E/2,x(tf)=E/2x˙(t1)=−v,x˙(tf)=−v$
(3)
And
$y(t1)=−hd,y(t2)=hL−hd,y(tf)=−hdy˙(t1)=0,y˙(t2)=0,y˙(tf)=0$
(4)
Based on the forms of the constraints, a cubic spline can be used for the x coordinate based on the constraints in Eq. (3):
$x(τ)=−E2−vτ+3E+3vtsts2τ2−2E+2vtsts3τ3$
(5)
where τ = t—t1, and ts is the duration of the swing phase (ts = tf—t1). The position in y can be divided into two sections with the constraints in Eq. (4), and the trajectory can then be defined using two cubic splines as follows:
$y(τ)={−hd+3hL(ts/2)2τ2−2hL(ts/2)3τ3,ifτ≤ts2hL−hd−3hL(ts/2)2(τ−ts/2)2+2hL(ts/2)3(τ−ts/2)3,ifτ>ts2$
(6)
Using these equations, the foot trajectory, x and y can be obtained for through the entire gait cycle using the following parameters:
$(stridelength)λ=E/β(frequency)f=v/λ(period)T=1/f=λ/vt0=0t1=βTts=(1−β)Ttf=T$
(7)
Figure 6 shows an example of a foot trajectory generated for E = 0.2723 m, hL = 0.153 m, hd = 0.7113 m, β = 0.81, and v = 0.043 m/s. The time points t0, t1, and t2 are shown on the top trajectory for clarity, where t2 is the time when the foot reaches hL. Note that the parabolic foot trajectory during swing is different from the foot trajectory in the standard human gait (in a shoe-like shape [35]) as a result of the gait planning algorithm described above. The foot velocity and acceleration of the swing phase are shown in Fig. 7. As shown in this figure, the velocity trajectories are smooth and continuous in both horizontal and vertical directions; the acceleration trajectories are continuous and mostly linear, with a single point of transition between different gradients in the vertical direction. Overall, the planned foot movement is smooth and easy to obtain with the joint motion controllers.

### 3.2 Leg Coordination.

For the coordination of leg movement in quadrupedal walking, the front legs (Leg 1 and Leg 3) are ½ T out of phase from each other; the rear legs (Leg 2 and Leg 4) are ½ T out of phase from each other; each front leg leads the rear on the same side by βT. Based on such phase relationships, a single dimensionless variable, namely, cycle ratio γ ϵ [0,1], can be defined to describe the progression in the gait cycle. The cycle ratio represents the proportion of the gait cycle that has been completed at the current moment, and for each leg, its specific gait ratio can be defined utilizing Eq. (8), assuming the quadruped system-level cycle ratio is defined based on Leg 1:
$[γ1,γ2,γ3,γ4]=mod([γ,γ+(1−β),γ+0.5,γ+0.5+(1−β)],1)$
(8)
where mod (ζ, 1) is to get the fraction part of ζ.

### 3.3 Varying Gait Parameters.

The cycle ratio defined above can be used to create a gait generator that generates the desired robot movement independent of the gait parameters. Specifically, the previous equations for the leg trajectories can be reformulated using the cycle ratio as the independent variable:
$vT=λΔtT=ΔγvΔt=λΔγtsT=1−β$
(9)
Substituting these equations into Eq. (2), the foot trajectory equations during stance can be converted into the following form:
$x(γi)=E2−λγiy(γi)=−hd$
(10)
where i = 1∼4.
For the swing phase, a new independent variable, μ, can be defined as μ = γiβ. With this new variable, the original cubic spline Eq. (5) can be rewritten as
$x(μ)=−E2−λμ+3E∓3λβ¯β¯2μ2−2E+2λβ¯β¯3μ3$
(11)
where $β¯=1−β$. Similarly, for the y coordinate
${−hd+3hL(β¯/2)2μ2±2hL(β¯/2)3μ3,ifμ≤β¯2hL−hd−3hL(β¯/2)2(μ−β¯/2)2+2hL(β¯/2)3(μ−β¯/2)3,ifμ>β¯2$
(12)
Finally, for the discrete time implementation of the gait generation algorithm, the gait ratio is updated with the following equations:
$Δγ=ΔtT=ΔtvβEγk←γk−1+Δγ$
(13)

### 3.4 Joint Trajectory Calculation.

The gait trajectories described above were generated in the operation (Cartesian) space. For the joint-level motion control, the spatial trajectories were converted to the joint angle trajectories using inverse kinematics. Based on the geometric relationships shown in Fig. 8, the knee joint angle can be calculated with the following equation:
$θ2=±2tan−1((l1+l2)2−(x2+y2)(x2+y2)−(l1−l2)2)$
(14)
where x and y coordinates are determined according to the spatial trajectories, l1 and l2 are the thigh length and shank length of the robotic leg, respectively. The sign of θ2 is selected based on the relative location of the leg (front or rear). The hip joint angle can be calculated based on the ϕ and ψ angles shown in Fig. 8, which are calculated with the following equations:
$ϕ=atan2(x,y)$
(15)
$ψ=atan2(l1sinθ2,l1+l2cosθ2)$
(16)
And the hip joint angle is simply the sum of ϕ and ψ:
$θ1=ϕ+ψ$
(17)

### 3.5 Joint Trajectories With Optimized Parameters.

Using the robotic leg trajectory generator described above, the joint trajectories can be solved for a walking gait based on a set of gait parameters. Parameters of the robot structure were determined during the design process, e.g., the lengths of the leg segments l1, l2. Parameters of the desired motion are pre-defined, such as is the desired height of the robot frame during walking hd and walking speed v. The parameters β (duty factor) and E (stroke length) must meet the requirements defined by Eq. (7), and the specific values can be determined through optimization. Here we used an optimal locomotion method developed in our previous work [36], which optimizes the quadrupedal walking with respect to the energy consumption. For the completeness of presentation, this approach is briefly described as follows. Using a cost function consisting of the COT and a term representing the ratio of a gait that the quadruped is not statically stable, we can find a gait suitable for this application. The cost function is evaluated numerically using quasi-static analysis to determine the joint torques required for support and the joint torques resulting from the dynamic effects. As such, we can solve for the cost function for a set of gait parameters (β, E) for a given desire velocity with an applied disturbance. The method of gradient descent was applied to find the optimal parameters for a desired velocity. The result of this optimization yields a gait defined by the following parameters: hd = 0.711 m, hL = 0.15 m, l1 = 0.394 m, l2 = 0.343 m, β = 0.81, E = 0.272 m, v = 0.043 m/s. The joint trajectories corresponding to this set of parameters are as shown in Fig. 9.

## 4 Real-Time Robot Control

For the real-time control of the robot, a distributed control system was constructed. For each joint, a microcontroller-based electronic circuit and the corresponding control program regulates the actuator output to obtain the desired joint motion. For the inter-leg coordination, a CAN bus was utilized for the communication of the individual joint controllers. Currently, one of the joint controllers also serves as the master controller, which broadcasts the start/stop commands as well as the synchronization signal. A schematic of the control system configure is shown in Fig. 10.

The joint controllers are all constructed with the standard proportional-integral-derivative (PID) control algorithm. Due to the use of different actuators, the controller gains were individually tuned based on the Ziegler-Nichols method [37], with subsequent trial-and-error adjustments. The controller gains implemented in the robot controller are summarized in Table 1.

## 5 Transitional Gaits

For the locomotion of a legged robot, the transition to a new steady state is a challenge from the control perspective. Unlike the steady-state gait, the transitional gait of legged locomotion is time variant, requiring timely adjustment of various gait parameters. Such challenge is especially obvious when the robot starts from a standing-still state, with zero velocities for all robot joints. To address this issue, a transitional gait planner was developed in conjunction with the gait generator described above, with the purpose of obtaining a smooth transitional gait before the steady state is reached. The transitional gait is essentially a gradually changing variation of the steady-state gait, with the related gait parameters gradually converging to the steady-state values in a coordinated manner.

The steady-state gait described in Sec. 3 involves two gait phases, stance and swings, that alternate in a gait cycle according to the duty factor β (the proportion of the gait in the stance phase). In comparison, when standing still, the feet of the robot are all in contact with the ground, implying 100% stance phase. To obtain a smooth transition, the duty factor decreases linearly from 100% to the steady-state value, as shown in Fig. 11(a). Correspondingly, the other control parameters (stroke length, lift height, etc.) also converge to their steady-state values linearly, with the only exception of the cycle period (which is adjusted once per cycle to maintain the consistency within each cycle). Figure 11 shows the changes of the control parameters in an example of the transitional gait, in which the transition is completed within five cycles. With this method, the transition from one steady state to another can be completed in a smooth and controlled manner. To demonstrate this point, the joint trajectories in the transitional gait are plotted in Fig. 12. As can be clearly observed in this figure, the magnitude and velocity of the joint motion gradually increase in the first five cycles and reach the steady state motion with well-coordinated patterns.

## 6 Experimental Results and Discussion

After the development of the Q-HARP robot and its control system, walking experiments were conducted to demonstrate the robot performance. The experiments were conducted in two phases. In the first phase, we conducted walking experiments of the robot to demonstrate its performance in joint motion control and the overall system control in steady-state gait, i.e., without implementing the transitional gait. In the second phase, we implemented the transitional gait at the beginning of each walking experiment, with the purpose of testing the robot’s ability to initiate the walking gait from a standing-still state.

### 6.1 Experiment of Steady-State Walking.

The purpose of this first-phase experiment is to test the joint-level performance to validate the gait planner and the joint motion controller. Having the robot operate in the steady-state condition simplifies the experiments by eliminating the effect of gait initiation. To allow the robot to reach a steady state without the risk of falling, the robot was lifted with two ropes (supported on moving anchor points in an overhead rail system) to allow the joints to move freely without touching the ground. The gait planner (Sec. 3) generated the desired joint trajectories based on a predetermined set of control parameters, and the joint controllers produced the actuator commands for joint angle tracking. After reaching the steady state, the robot was slowly lowered to the ground while keeping the robot frame steady and horizontal, and then started walking independently. The video2 attached to this paper shows the walking performance, with the gait generated based on the following parameters: hd = 0.711 m, hL = 0.15 m, β = 0.81, E = 0.272 m, v = 0.043 m/s.

The joint-level control performance is shown in Fig. 13, in which the desired versus measurement joint angles were compared for each robotic joint. As can be clearly observed in each plot, the measured joint trajectories match the corresponding desired trajectories closely. Within the same cycle, the tracking error in the stance phase is slightly larger than that in the swing phase, presumably due to the heavier load in stance. The tracking error, nonetheless, remains at a very low level, providing a solid basis for the system control task of obtained the desired gait. To quantify the system-level control performance, the primary metric is the spatial rotation angles (roll/pitch/yaw), which should be minimized to maintain the stability of the robotic platform. We attached an inertial measurement unit (MPU 6050 InvenSense, San Jose, CA) to the robot frame for the measurement, with the typical results shown in Fig. 14. As can be observed from the curves, the spatial rotation angles were kept under 1.0 deg during the majority of the gait cycle. Such high level of stability clearly demonstrates the effectiveness of the gait generator and the robot motion controller.

### 6.2 Experiments of the Transitional Gait.

In the second-phase experiments, we shifted the focus to the testing of the transitional gait. Unlike in the first phase, the robot starts from a standing-still position, with all feet on the ground providing stable support to the robotic platform. With the transitional gait described in Sec. 5, the robot gradually transitioned to the steady-state walking gait in the first five cycles (approximately 1.1 m travel distance), and then walked in the steady-state gait once the transition was completed. The video attached to this paper also shows the performance of such transitional gait, and the joint-level and system-level control performances are shown in Figs. 15 and 16. As shown in the desired versus measured joint trajectory plots (Fig. 15), the joint motion controllers provide consistent control performances in both transitional and steady-state walking, with very small errors throughout the entire gait cycle. On the system level, the spatial angles (pitch, yaw, and roll) in the transitional gait are smaller than that in the steady-state gait as shown in Fig. 16, presumably due to the slower joint movements when the magnitude of joint movement increased in the transition. Overall, the consistently small spatial rotation of the robotic platform clearly demonstrated the stability of the robotic platform and the effectiveness of the robot control system.

### 6.3 Discussion.

The experiments demonstrated the basic performance of the robotic platform as well as the effectiveness of the gait planning and motion control algorithms. The legged locomotion provides a superior performance in overcoming obstacles and terrains compared with conventional wheeled locomotion. With a robotic leg design mimicking the human biological legs, the Q-HARP is expected to provide a similar capability to humans in such challenging locomotion tasks. Due to the limitations in sensing and control, such capability has not been explored in this work, but the related research is planned as part of the future work. In addition to the robot design, this paper also presents a novel method of kinematic analysis that integrates the classic theory of quadruped stability (e.g., COM in support polygon), quadruped gait planning, human leg kinematics, and the method of mathematic smoothness (e.g., interpolation of cubic splines). The method of setting varying gait parameters is also innovative as it simplifies the processing of digital control and makes the gait transition feasible and smooth. For the future work, the authors plan to further explore the Q-HARP’s capability in assisting human walking and overcoming obstacles and terrains by using advanced sensing methods to measure the environment as well as the human–robot interaction forces, developing novel control approaches for effective human interaction and environmental adaptation, and conducting the related experiments of human assistance in various environments.

## 7 Conclusions

In this paper, the authors presented the design, gait planning, and motion control of Q-HARP, a novel quadrupedal robotic platform intended for the assistance of mobility-challenged individuals. As numerous joints are needed to construct the robot hardware, the authors focused the design work on the powered hip joints, for which a powerful flat motor powers the corresponding joint through a novel two-stage chain drive. The powered knee joints, on the other hands, were essentially the robotic prosthetic joints developed in the authors’ prior works. To enable the robot to maintain a stable walking gait (in preparation for the future human assistance), the authors developed a gait generator to generate a statistically stable gait with multiple adjustable parameters, which were determined with an optimization method. A transitional gait was also developed, with the purpose of providing a stable and smooth transition before the steady-state walking is reached. For the real-time control of the robot, the authors constructed a distributed system, in which a microcontroller-based motion controller is implemented for each joint, and the standard CAN bus is used for inter-joint communication and coordination. Finally, the Q-HARP robot was experimentally tested to quantify its control performance in both steady-state and transitional walking. The joint-level and system-level performances demonstrated that the robot is able to provide a stable and smooth walking performance based on the effective gait planning and joint motion control.

## Acknowledgment

The authors gratefully acknowledge the support of the National Institutes of Health under Grant No. R01 NR016151 and the National Science Foundation under Grant No. 1351520.

## Conflict of Interest

There are no conflicts of interest.

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