2.1. Types of gait generation techniques

Fundamentally, there are four gait generation techniques; model-based, natural dynamics-based, bionic kinematics or biological mechanism-based, and stability criterion-based technique (see Fig. 4). The model-based gait generation technique mainly consists of interpolation-based gaits which means generating reference trajectories by polynomial satisfaction of the constraints and tracking them by using the control system [Reference Vanderborght, Van Ham, Verrelst, Van Damme and Lefeber42]; linear inverted pendulum model (LIPM) dynamics-based modeling and optimization-based gaits that include the optimization of energy consumption, robot construction, control system, and adaptation. The drawback of this technique is the requirement of all the information on the dynamic parameters of the respective biped model.

It is to be noticed that the biological mechanism-based gait generation is inspired by animal and human motion capture data (HMCD) which can generate different stable rhythmic patterns along with the capabilities to change the pattern and its speed quickly [Reference Matsuoka43]. Further, the central pattern generators (CPG) and neural networks (NN) are inside the spinal cord, capable of generating rhythmic locomotion and lacking any sensory signals. The Matsuoka neural oscillator [Reference Pandy, Anderson and Hull44] and the Van der Pol oscillator [Reference Zielińska45, Reference Or and Takanishi46], two popular models, are used for modeling the CPGs. It has been observed that the other approaches which are biologically inspired fall under artificial intelligence (AI)-based gait, which encompasses genetic algorithms (GA), fuzzy logic (FL), and NN.

Moreover, natural dynamics-based gait is performed based on intuitive control, natural dynamics of the biped, physics of the system, and virtual elements like dampers and springs that is why this technique does not need any predefined reference trajectories [Reference Al-Shuka, Allmendinger, Corves and Zhu47]. And also, the gait can be performed based on stability criterion-based gait generation techniques, including ZMP, DBM, CoP, COG, CoM, FRI, theory of capture points, foot placement estimator, periodicity-based gaits, and limit cycle analysis.

Apart from these gait generation techniques, the researchers should also identify some factors (see Fig. 4) while planning the gait generation of the biped robot, such as a suitable trajectory equation based on polynomial, cycloidal, and Bezier curves, avoiding static and dynamic obstacles for path planning, and types of terrain for estimation of the boundary conditions for swing foot, hip, and wrist trajectories.

2.2. Biped robot design and its challenges

The above discussion of fundamental gait generation techniques might help the researchers to identify standards and best practices for developing the biped robot and generating its gait on different terrains. This partially fulfills Objectives I and II of this research work. The fundamentals of biped locomotion have been explained briefly in the introduction part of this article. At the same time, the design issues of the biped robot have been presented pictorially in Fig. 5, which needs to keep in mind before planning and designing the biped robot. These factors also affect the ability of a robot to walk over uneven terrain. The fundamentals of modeling the biped robot, such as deciding the number of degrees of freedom of the robot, include the allocation of the actuators and their orientations. Further, the type of trajectory must be planned for each part of the robot’s mechanism, such as the swing foot, wrist end, and hip, to enable the robot to move from the source to the aimed position, that is, path planning. The analytical modeling could be of the planner type, which includes trajectory planning only for the sagittal plane, whereas trajectory planning for both the sagittal and frontal planes or the sagittal, frontal, and horizontal planes, that is, 3D modeling must be done to enable the robot to walk in a real environment. In addition to, researchers discussed various types of walking patterns, type of foot and ground contact, including probable forces developed due to the impact of the heel on the ground, and arrangement of heel and toe contact with the ground when planning the dynamics for improved stability robustness. Other than these, elastic and stiff links of robot may benefit with some flexibility to absorb impact and cause instability because of the uncertain motions generated by the elasticity factor. However, the mobility of the links depends on active or passive joints. Moreover, various stability criteria as per their skills, such as ZMP, CoP, COG, FRI, can be possible to adopt. Therefore, the mathematical model of the biped robot consists of kinematics and dynamics by using any high-level programming language and also build their planned model with the help of software, such as CoppeliaSim, ROS, MATLAB, to do simulation and verify the feasibility of their planned model. Additionally, the researchers must concentrate on the characteristics of environments or terrains, optimization algorithms, autonomous navigation through biologically inspired learning algorithms for suitable decision-making and adaptivity, designing the controller as per the nonlinearity present in the robot’s mechanism, suitable gait generation techniques, the number of underactuated and overactuated joints, planning the robustness against the probable unbalanced external forces, and both online and offline modes of tracking the deviation of the trajectories from the planned mathematical model. In addition to planning includes the hardware of the robot consists of structure of the robot, sensors for recording real-time data, and microcontrollers for operating the actuators, which could be electric, hydraulic, or pneumatic drives. Over and above, some challenges observed while designing the biped robots are as follows:

• • The biped robot joints are underactuated during SSP and overactuated during DSP [Reference Chevallereau, Bessonnet, Abba and Aoustin48]. Consequently, the dynamics and control laws are also changed during this phase transition. In addition to the above problem, the biped robot acts as an open chain mechanism in SSP and a closed chain mechanism in DSP, which consequently changes the dynamics equations to be used.

Remark: Over-actuation of the biped mechanism is controlled by kinematic Jacobian [Reference Vanderborght, Van Ham, Verrelst, Van Damme and Lefeber42, Reference Shih and Gruver49] and minimization of the joint torques by algebraic optimization [Reference Sano and Furusho50]–[Reference Zhu53]. However, the continuous dynamic response can still not be guaranteed [Reference Al-Shuka, Allmendinger, Corves and Zhu47]. Similarly, the problems that occurred during the SSP phase are encountered by using the four control techniques: port-Hamiltonian method [Reference Duindam and Stramigioli54, Reference Duindam and Stramigioli55], differentially flatness-based approach [Reference Sangwan and Agrawal56], hybrid zero dynamics (HZD) [Reference Westervelt, Grizzle and Koditschek57], and time scaling method [Reference Zhu53, Reference Chevallereau58].

• • A humanoid robot can be made up of more than 30-DOF, which makes its stability and control more complex [Reference Zhu53, Reference Raibert, Tzafestas and Tzafestas59, Reference Park, Kim and Oh60].

• • When the biped robot is walking in various unknown environments in real time, it needs to develop robust algorithms for possible external disturbances and noises.

Remark: Therefore, online real-time adaptive strategies could be the possible solution.

• • Unexpected shocks and instability of the robot are happened due to stiff joints [Reference Vanderborght, Van Ham, Verrelst, Van Damme and Lefeber42]. Many researchers have used elastic joints to overcome the problem, which can be preferred and consequently increase the system’s DOF due to flexible joints.

Remark: Despite the complexity of making the biped mechanism closer to imitating human walking, compliant legs are employed [Reference Al-Shuka, Allmendinger, Corves and Zhu47].

• • The foot-ground contact needs to be designed appropriately to avoid impulsive forces.

To overcome these challenges, the author suggests to use a suitable controller other than the right selection of gait generation methodology.

2.3. Controllers used for generating the smooth gait

Many researchers have developed various control algorithms to control the motions and dynamic balancing of the biped robots for smoothly coordinated motions among the different mounted motors in every joint. The authors have discussed popular controlling techniques such as PID, CTC, NN, CMAC-NN, FLC, MPC & impedance control in this section.

3.1. Gait generation on the flat terrain

While performing the gait of the biped robot on a flat surface, several issues need to be fulfilled to complete one walking cycle. The most crucial aspects of walking are balancing, controlling, trajectory synthesis, and foot-ground interaction. Figure 6(a) and (b) show the gait generation of the biped robot on a flat surface with interpolation of cubic polynomial trajectory for the swing leg [Reference Mandava and Vundavilli90]. Various methodologies for biped gait generation are being discussed here based on four fundamental gait generation techniques adopted by researchers.

Fig. 6.

Schematic diagram showing mass, length, and angles of each links (a) 9-DOF biped robot walking on the flat terrain [Reference Hurmuzlu, Génot and Brogliato159], (b) biped robot walking on the flat terrain [Reference Mandava and Vundavilli90].

Most of the researchers adopted the model-based gait technique for walking on flat terrain, which is the simplest case compared to any other terrain. The dynamics laws for the biped robot were determined by using the fundamentals of LIPM [Reference Vukobratović and Stepanenko3, Reference Xie, Zhao, Sun, Yang and Li26, Reference Golliday91–Reference Khan, Li and Zhou123], virtual height inverted pendulum mode [Reference Ha and Choi111], Euler-Lagrange formulation [Reference Hemami and Wyman124]–[Reference Mandava and Vundavilli132], Newton-Euler approach [Reference Navaneeth, Sudheer and Joy133], and then after calculation of the dynamics, the whole-body gait can be generated by using forward and inverse kinematics [Reference Kurcmatsu, Katayama, Iwata and Kitamura99, Reference Hernández-Santos, Rodriguez-Leal, Soto and Gordillo128, Reference Mandava and Vundavilli132, Reference Shih, Li, Churng, Lee and Gruver134–Reference Ceranowicz147]. The complexity of the biped modeling can be dealt by arranging the hip, knee, and ankle joints of the biped model as underactuated [Reference D.A.Bravo and Rodas125, Reference Cambrini, Chevallereau, Moog and Stojic148, Reference Chevallereau, Aoustin and Formal’sky149] and frictionless [Reference Townsend and Seireg150, Reference Formalsky, Morecki, Bianchi and Jaworek151]. Interpolation of the joint trajectory is also adopted for gait generation. Chevallereau et al. [Reference Chevallereau, Aoustin and Formal’sky149] obtained optimal joint reference trajectories gait cycle by using fourth-order polynomial functions for joint variables while keeping ankle joint underactuated. The reduced ankle power was compensated by the motion of swinging leg and body for proper foot contact with the ground, smooth walking was obtained for the lesser complex biped model, and also dynamically stable bipedal gait over the flat terrain was obtained [Reference Yi and Zheng152]. Similarly, the authors [Reference Mandava and Vundavilli132, Reference Kumar, Lathan and Vundavilli139–Reference Mandava and Vundavilli141, Reference Mandava and Vundavilli145, Reference Sabourin and Bruneau153, Reference Mandava and Vundavilli154] assigned cubic polynomial trajectories for the swing foot, hip, and wrist joint of 18-DOF humanoid robot.

Numerous researchers have developed many control schemes to reduce the effect of nonlinearities in the biped mechanism due to complex dynamics. Therefore, nonlinear feedback control for 5-DOF biped model while moving in air and free fall motion [Reference Hemami and Zheng155]; closed-loop eigen structure assignment for prescribed gait of 5-DOF model [Reference Ceranowicz146, Reference Ceranowicz147]; two-level control scheme for generating prescribed gaits and motion to reduce large deviations [Reference Vukobratović, Hristić, Stokić and Gluhajić156]; control scheme based on a novel integration of the multiple input & multiple outputs (MIMO) framework for 10-DOF biped model [Reference Kljuno and Williams136]; control technique by selecting state variables dependent output functions such as angular orientations and velocities along with Pfaff-Darbous principle and differential geometric tools [Reference Cambrini, Chevallereau, Moog and Stojic148]; robust control technique based on series elastic actuation in “FLAME” & “TUlip” for limit cycle walking [Reference Hobbelen, de Boer and Wisse157]; local feedback at each joint of the robot [Reference Furusho and Masubuchi95] and feedback control scheme for stable cyclic gait [Reference Gubina, Hemami and McGhee28] developed to obtain the dynamic stability of the biped walking on flat terrain. Other than these, a technique based on wireless monitoring and controlling of actuators and sensors by employing the tunneling method was introduced by Nicolau et al. [Reference Nicolau, Albero, Blanes and Simó158] for robot YABIRO, which is done by employing the tunneling method for enclosing CAN messages into a TCP/IP network over WiFi. Similarly, the author in ref. [Reference Oh, Sim, Jeong and Oh143] developed an online adaptation technique based on a set of intuitions for tracking reference trajectories.

Researchers have also attempted to optimize the energy consumption for obtaining the periodic gaits [Reference Hardt, Kreutz-Delgado and Helton160] by using Hamilton-Jacobi-Bellman type equations and obtaining the gait. It has been found that the gait transition from running to regular walking by releasing extra energy while shortening the legs [Reference Hodgins161] with the help of an antagonistically driven hip joint consisting of two nonlinear springs, two AC servo motors and one free joint. Furthermore, Ji et al. [Reference Ji, Qian, Ren and Ren162] investigated the impulsive effects of the ankle push-off by accelerating the swing leg and decreasing the changes in COM speed to increase the gait speed.

When the model’s physics helps to generate the gait, it is termed natural dynamics-based gait. In the initial time of biped development, the researchers preferred the physics-based gait due to the unavailability of intelligent techniques such as passive pendular gaits in the swinging phase [Reference Sardain, Rostami and Bessonnet163]; forward and reverse walking of BIPER-1, 2, 3, 4 & 5 [Reference Miura and Shimoyama93]; virtual spring and a damper to the prevalent inverted pendulum-based biped robot [Reference Bae and Oh117]; intuitive gait strategy for 9-DOF biped model controlled by forces and posture [Reference Muscato, Spampinato and Costa164] and the virtual constraints for the able gait of 7-DOF biped model RABBIT [Reference Canudas-de-Wit165].

A few approaches related to stability criterion-based gait were also reported. In ref. [Reference Kagami166], the author developed “Humanoid H7” for mimicking human motions by tracking ZMP trajectories and generating stable gait by modifying the horizontal COG positions efficiently with the help of dispersed force sensors, motion capturing mechanisms, and force plate. Further, the author [Reference Li, Takanishi and Kato167] obtained the ZMP by using the universal force-moment sensor on WL-12RIII. In addition, Tagawa and Yamashit [Reference Li, Takanishi and Kato167] introduced the Zero Moment Joint (ZMJ) concept and showed a stable biped gait for the 8-link biped model when ZMJ was the only ankle joint.

Apart from the above-discussed approaches, few researchers have also generated the biped gait inspired by bionic or biological mechanism-based gaits, which are discussed here. Such as, Yazdani et al. [Reference Yazdani, Salarieh and Foumani168] developed a bi-layer controller consisting of high-level and low-level controllers. The high-level controller utilizes all sensory information to deal with the dynamics and produce stable rhythmic motions through conscious learning during training. The low-level controller consists of a control network in which every individual node is an oscillatory dynamic that learns and reproduces the desired paths. The critic agent in the node allocates a particular controller for any parameter based on its eligibility. The proposed controller proved robust and stable as a dynamic controller but mainly featured as a path or trajectory-based controller. Similarly, the nonlinear oscillator has also been used to observe the sensor output to obtain real-time online trajectories [Reference Héliot and Espiau169]. Apart from the above-mentioned gait generation strategies, other important approaches have been listed in Table II.

Table II.

Various approaches for multi-DOF biped robot’s gait generation on a flat surface.

Gait generation techniques: ^a Model based gaits; ^b Biological mechanism-based gaits; ^c Natural dynamics-based gaits; ^d Stability criterion-based gaits.

Controllers implemented: ¹ PI; ² PD; ³ PID; ⁴ FLC; ⁵ Inverse Delta-P Unit; ⁶ CTC; ⁷ Programmable Logic Controller (PLC); ⁸ MPC; ⁹ Analogue; ¹⁰ NN.

3.2. Gait generation on ascending and descending the sloping terrain

Gait generation of the biped robot on a sloping surface is a more challenging task than the flat terrain. Figure 7 (a) and (b) show the biped robot’s gait generation in ascending and descending the sloping surface.

Fig. 7.

Gait generation on a sloping surface (a) ascending the slope and (b) descending the slope [Reference Gong and Schiehlen215].

Very few researchers have reported the model-based gait generation approach for ascending and descending sloping terrain. Kuo [Reference Kuo109] developed an analogy of human gait with an inverted pendulum, provided a circular trajectory instead of a horizontal trajectory for COM, and found that a horizontal COM trajectory consumes more muscular energy.

In addition to what has been said, Pratt [Reference Pratt212] presented the natural dynamics and inherent robustness of the biped locomotion mechanism and developed the Spring Flamingo robot using a low-impedance controller which can start and stop while moving on slopes and rolling surfaces with various speeds. The derived control algorithm exhibits three stages: the primary algorithm control walking, the secondary algorithm exploits the kneecap, ankle, and passive swing leg natural dynamics, and the tertiary algorithm ensures fast walking of the swing leg. The authors added lateral balance to the three-dimensional algorithm and simulated the 3D model.

Stability criterion-based approaches have also been developed and implemented for gait generation on a slope. Massah et al. [Reference A.M., A.S., Salehinia and Najafi113] used 3D inverted pendulum-based equations and ZMP concept for developing a trajectory planner by employing the semi-ellipse EOM (equations of motion) for an NAO humanoid robot and simulated on Webots while walking on various slope terrains. Vundavilli and Pratihar [Reference Vundavilli and Pratihar127] used ZMP concept and reported more DBM for ascending the slope than descending the slope. Furthermore, Hwang et al. [Reference Hwang, Yeon and Park213] obtained momentum equations based on ZMP by treating biped robot as a particle and assuming the motion of CoM parallel to the slope and then simulated it by using ResurDyn and MATLAB commercial software. In addition to, Ito et al. [Reference Ito, Nishio, Ino, Morita, Matsushita and Sasaki214] reduced the number of actuators of biped robot without sacrificing adaptability and ability then applied the gravity compensation mechanism and feedback from CoP of the ground reaction forces.

Most of the researchers have attempted the biological mechanism-based gait for ascending and descending the sloping terrain. The central pattern generator (CPG) has inspired the researchers to build learning architecture for biped robots of different configurations and enabled the biped robots for autonomous biped gait [Reference Zheng10]; smooth gait transition from flat to slope & vice versa [Reference Zheng and Shen217]; walking on a flat plane with different friction properties and little change in inclination [Reference Nakanishi, Morimoto, Endo, Cheng, Schaal and Kawato218], stable gait on unknown inclination [Reference Song and Hsieh219], and adaptivity in different environments [Reference Macedo, André and Santos220]. Further, few gait generation algorithms have been developed for generating complex gait patterns using AI techniques such as Genetic Algorithm [Reference Hasegawa, Arakawa and Fukuda221], neurons and neural pathways [Reference Maniscalco, Messina and Storniolo222], genetic-neural (GA-NN) and genetic-fuzzy (GA-FLC) [Reference Vundavilli and Pratihar223], NN integrated with modified chaotic invasive weed optimization (MCIWO), and PSO algorithm [Reference Mandava and Vundavilli224]. The AI has enabled the biped robots to walk on sloping terrains more efficiently, but if there is a change or increase in inclination angle, then some essential sensors must be attached to the biped legs. The researchers have employed the integration of position sensors (on joints) and force sensors (under foot) to identify slope gradient [Reference Zheng and Shen217]; gyroscope and accelerometer sensors to identify the upper body’s posture [Reference Song and Hsieh219]; inertial measurement unit (IMU) sensor [Reference Behera, Mandava and Vundavilli216] (gait shown in Fig. 8); and 2-axes accelerometer sensor [Reference McGrath, Baltes and Anderson225] for obtaining the smooth, balanced gait on slope terrain. To overcome the difficulty due to complex mathematical modeling, the author [Reference McGrath, Baltes and Anderson225] developed a collective balancing reflex of threshold, PID, and hybrid control with a 2-axes accelerometer sensor, which does not need any mathematical modeling. The remaining methodologies are briefly summarised in Table III in addition to the methods already mentioned.

Table III.

Various approaches for multi-DOF biped robot’s gait generation for ascending and descending on the sloping terrain.

Gait generation techniques: ^aModel based gaits; ^bBiological mechanism-based gaits; ^cNatural dynamics-based gaits; ^dStability criterion-based gaits.

Controllers implemented: ³PID; ⁴FLC; ¹⁰NN.

Fig. 8.

Dynamic stability against gravity on the sloping terrain [Reference Behera, Mandava and Vundavilli216].

Remark: Due to the enhanced complexity of the terrain, scientists have shifted their gait generation approaches from model-based gait to advanced AI-based or bionic gait generation techniques and obtained better adaptivity. Many researchers have adopted biological mechanisms and stability criterion-based methods for generating biped gait on sloping terrain.

3.3. Gait generation on ascending and descending the staircase

The gait generation on the staircase is very different from the flat and sloping surfaces due to the approximate relationship between the height-width of every step and the length of the robot’s leg. There are chances of collision of the robot with the staircase. Therefore, the swing phase take-off mechanism is essential in determining the gait pattern characteristics [Reference Townsend and Tsai230]. The synchronization of all robot links and defining the proper foot trajectory become vital for stabilizing the robot. Figure 9(a) and (b) show the gait generation of the biped robot for ascending and descending the staircase, respectively, by controlling the forward gaits speed and swing foot placement.

Fig. 9.

Schematic diagram showing the gait generation of the biped robot (a) ascending the staircase and (b) descending the staircase [Reference Mandava and Vundavilli145].

In the early development stage of the biped robots, a 17-DOF biped robot consisting 15 active DOF and 2 passive DOF was developed by Espiau et al. [Reference Espiau231] under the French joint project BIP that achieved walking on flat terrains, inclined terrain, ascending, and descending stairs. Since then, many approaches and models have been developed and shown their improved robustness. Tzafestas et al. [Reference Raibert, Tzafestas and Tzafestas59] reported that the sliding mode control performs better than the torque-based "pure CTC" technique to overcome the high nonlinearities of gaits on the staircase. In this direction, Albert [Reference Albert232] developed a trunkless biped robot BARt-UH and designed a path planning mechanism to optimize nonlinearities.

Some researchers have obtained stability by controlling the motion of the CoG of 7-DOF biped with large feet [Reference Shih233] and supervising of the ground center of pressure (GCoP) of 12-DOF biped by using the “hybrid-state driven autonomous control (HyDAC)” algorithm [Reference Zachariah and Kurian234]. Besides that, Mousavi and Bagheri [Reference Song and Hsieh219] developed a mathematical model for interpolating third-order spline and monitoring the ZMP using MATLAB/SIMULINK. A fusion of model-based gait and bionic or AI-based gait was reported in refs. [Reference Mandava and Vundavilli235, Reference Mandava and Vundavilli145]. Later, Mandava and Vundavilli developed an optimal PID controller for an 18-DOF mini-sized humanoid robot and reported its better performance when optimized by a novel MCIWO algorithm than PSO. The developed algorithm also encompasses the deviations in slope inclination and staircase dimension. The authors reported enhanced DBM due to cubic polynomial trajectory in swing foot and reduced hip height and increment in the height of the stair slope.

Bionic gaits consisting of AI-based approaches helped the researchers generate adaptive and autonomous gaits. Intelligence has been developed in biped models by implementing multi-layered Hopfield kind NN, which resulted in autonomous trajectory generation [Reference Kurcmatsu, Katayama, Iwata and Kitamura99]; architecture of building blocks comprising Reconfigurable Adaptive Motion Primitives (RAMPs) [Reference Rakovic, Borovac, Santos-Victor, Batinica, Nikolic and Savic236]; controller consisting of numerous neurons for energy efficient gait of NAO robot and managing small disturbances [Reference Sun and Roos237]; FLC rule base optimized by GA [Reference Jha, Singh and Pratihar238] and controller composed of NN and FLC [Reference Zhong and Chen239]. Zhong and Chen [Reference Zhong and Chen239] reported that the MPSONN (Neural Network optimized by Modified Particle Swarm Optimization) required the least training time compared to MPSOFLC, PSONN, PSOFLC, and NN. And also, the authors [Reference Mandava and Vundavilli90] demonstrated better performance of the NN when optimized by MCIWO than differential evolution (DE) and PSO. For remaining biped gait generation techniques not covered in this section, see Table IV.

Table IV.

Various approaches for multi-DOF biped robot’s gait generation for ascending and descending the staircase.

Gait generation techniques: ^a Model based gaits; ^b Biological mechanism-based gaits; ^c Natural dynamics-based gaits; ^d Stability criterion-based gaits.

Controllers implemented: ³ PID; ⁴ FLC; ⁶ CTC; ¹⁰ NN.

3.4. Gait generation for avoiding, crossing, and stepping over the obstacles

The evolution of biped locomotion has the motive to develop a robust humanoid robot, efficient enough to perform all human motions. Humans inherit learnings from all sensory, intuitive knowledge, which is challenging to produce in the humanoid robot. But, applying some reinforced learning (RL) algorithms can develop intuitiveness in humanoid robots. To do so, many researchers have proposed some unique methodologies.

Most of the researchers have shown interest in path planning to avoid obstacles. Very few have attempted to solve the problem of identifying the obstacles, and then crossing over or stepping over the obstacles. The perception-based control system was developed for generating walking primitive data of 16-DOF biped robot for step length adaptation, altering the direction and stepping over the obstacles in ref. [Reference Denk and Schmidt245]. And also, the architecture consisting of the GA-NN and DE-NN that means NN trained by GA and DE, respectively, achieved the gait for crossing over the obstacles and positioning the foot on the obstacles as shown in Fig. 10(a) and (b) along with generating the horizontal trajectory for hip and cubic polynomial trajectories for the swing foot respectively [Reference Kumar, Lathan and Vundavilli139]. Gait while crossing the obstacles showed a more robust gait than positioning the foot on top of the obstacles.

Fig. 10.

Stick diagram showing the gait generation (a) crossing the obstacle, (b) stepping over the obstacle [Reference Kumar, Lathan and Vundavilli139].

Vukobratović and Stepanenko [Reference Vukobratović and Stepanenko246] used the concept of prescribed synergy for more realistic locomotion. Then in 1989, the scientist Raibert et al. [Reference Raibert, Brown, Chepponis, Koechling and Hodgins247] from the Massachusetts Institute of Technology, developed a control system for one-legged locomotion and extended it to a planar biped machine for running, negotiating obstacles, and climbing stairs. The open-loop control was integrated with the usual running gait that generated front flips and aerials motion. Igarashi and Nogai [Reference Igarashi and Nogai248] generated adaptive walking patterns and trajectories for a lower limb biped robot with a step of 1.5 seconds and 0.3 m width against variation in width, an obstacle, ascending staircase and descending staircase also. Later, the author [Reference Kashyap and Parhi249] obtained LIPM plus flywheel model (LIPPFM) optimized by ant lion optimization (ALO), which relaxes the constraint of COM’s height; consequently, a larger stride gave a more robust gait for avoiding the obstacles, as shown in Fig. 11.

Fig. 11.

Experimental & simulation result of navigation scheme [Reference Kashyap and Parhi249].

In addition to said methodologies, the self-navigation of biped robots has also been studied for a long time. Detecting the perception of the terrain is a very complex impediment for biped robot’s navigation due to the limited view angle of visual sensors [Reference Lee, Lee, Hwang and Park250]. That is why most of the navigation approaches are based on AI for the identification of the obstacles and then navigation around them for avoiding the obstacles. Such as, a novel hybridization framework consisting of a regression controller optimized with ant colony optimization (ACO) [Reference Kumar, Sahu and Parhi251]; ZMP evaluation by using visual sensors [Reference Yagi and Lumelsky252]; multi-modal sensory architecture having 6-DOF force-torque sensors at robot ankles and joint encoders for identifying the contact of the foot with a block [Reference Lee, Lee, Hwang and Park250]; RA-FLC hybrid controller integrated with the Petri-net model and a control software consists of a stereo-camera driver [Reference Kumar, Muni and Parhi253]; FL intelligent algorithm [Reference D’Apolito183, Reference Rath, Parhi, Das, Muni and Kumar254]; integrated intelligence navigation controllers based on regression analysis and genetic algorithm approach for single and multiple NAO humanoid robots [Reference Kumar, Kumar and Parhi255]; a pure vision-based algorithm for the entire humanoid navigation strategy based on the topological map or visual memory (VM) by using an RGB-D camera [Reference Delfin, Becerra and Arechavaleta256] and 3D-SLAM (Simultaneous Localization and Mapping) by evaluating the next viewpoint from a map through the camera for finding and holding the aimed object in unknown surroundings [Reference Tsuru, Escande, Tanguy, Chappellet and Harad257]. Besides the said approaches, the rest of the methodologies have been collected and tabulated concisely in Table V. Over and above the static obstacles, other strategies for dynamic obstacles have been discussed in Section 3.5.

Table V.

Various approaches for multi-DOF biped robot’s gait generation for avoiding, crossing, and stepping over the obstacles.

Gait generation techniques: ^aModel based gaits; ^bBiological mechanism-based gaits; ^cNatural dynamics-based gaits; ^dStability criterion-based gaits.

Controllers implemented: ³PID; ⁴FLC; ⁸MPC; ¹¹Petri-Net; ¹²Hybrid RA-FLC; ¹³Kalman Filter; ¹⁴Gaze Control.

3.5. Gait generation for avoiding the dynamic obstacles

Many pieces of research have been carried out regarding the obstacles on the path of any biped robot. The proposed techniques and framework are efficient for avoiding, crossing, or stepping over stationary or static obstacles but do not consider moving or dynamic obstacles, representing a more realistic picture of walking in the natural environment. In this direction, Kashyap et al. [Reference Kashyap, Parhi, Muni and Pandey259] proposed an integrated DWA-TLBO (Dynamic-Window Approach and Teaching Learning Based Optimization) algorithm where positioning of target and obstacles are given to DWA as input for optimizing the speed and intermediate in-between consequences to TLBO and collectively evaluated optimum turning angle for avoiding the obstacles as shown in Fig. 12(b). The static navigation considers NAO, a mini-sized humanoid robot and stationary obstacles. In contrast, dynamic navigation considers several NAO robots where each NAO works as a dynamic obstacle for others with the help of a hybrid regression FL control approach, as shown in Fig. 12(a). The researchers designed and applied a Petri-net controller in every NAOs to avoid clashing and validated the simulation and experiment results.

Fig. 12.

Experiment for self-navigation (a) by employing hybrid regression fuzzy logic control [Reference Kumar, Muni and Parhi253] (b) by employing hybrid DWA-TLBO [Reference Kashyap, Parhi, Muni and Pandey259].

Remark: This approach can lead us to develop a quick and robust architecture for a humanoid robot to move in real environment and work like human beings. Still, as per this research, one can observe that a typical network helps to identify the safe route and avoid collisions. At the same time, one cannot have networked with everything in the natural environment. Object detection by employing visual sensors and some RL algorithms makes it possible to work in a real-time environment for a humanoid robot. Furthermore, the gait generation for crossing the ditches has been explained in the next section.

3.6. Gait generation for crossing over the ditches

The gait generation for crossing the ditches has been studied by only a few researchers, which is discussed in this section. Vundavilli and Pratihar [Reference Vundavilli and Pratihar268] together proposed a gait planner for ditch crossing based on analytical modeling and two other techniques; NN and FL-based optimization of the dynamic balance margin and energy consumption for a 7-DOF biped robot. The NN and FL-based gait planners are trained offline by GA, enabling optimal online gait generation. The approaches other than the analytical modeling are more adaptive and more balanced for the minor energy consumption of a biped robot. In addition, Janardhan and Kumar [Reference Janardhan and Kumar269] developed a multibody dynamics framework for gait generation of 5-DOF biped robot as shown in Fig. 13(a), for giant steps and walking across wide ditches of width more significant than the leg length. The paths are produced using time-independent constraints based on the distance trekked by COM. The approach is suitable for a robot similar to an adult human for going across the ditch of 1.05 m width with 0.2 lowest coefficients of friction. Later on, Janardhan and Kumar R [Reference J. and P.K.270] again proposed an approach for generating the dynamically balanced ditch crossing gait of width equal to or more than the length of the leg of a 7-DOF biped robot. The developed algorithm is incorporated with adopted constraints and adaptively tunes the time. Figure 13(b) shows that the simulation gave optimal joint torques and angle trajectories. For better understanding, these approaches have been listed concisely in Table VI. Similarly, the challenges and approaches for gait generation on uneven terrains have been presented in the next section.

Fig. 13.

Stich diagram of gait generation for crossing ditch (a) SSP, DSP [Reference J. and P.K.270] & SSP [Reference Janardhan and Kumar269] (left to right) phases of ditch crossing, (b) simulation of biped robot crossing ditch [Reference J. and P.K.270].

Table VI.

Various approaches for multi-DOF biped robot’s gait generation for crossing the ditches.

Gait generation techniques: ^bBiological mechanism-based gaits.

Controllers implemented: ⁴FLC; ¹⁰NN.

3.7. Gait generation on the uneven terrains

Locomotion modeling on uneven terrain is challenging for modeling due to its uncertainties and not having specific patterns. That is why the foot placement is challenging to maintain dynamic balancing for biped robot walking on uneven or rough terrain. In this direction, worldwide researchers have developed LIPM-based biped model of massless legs [Reference Kajita and Tani97]; LIPM-based simplified model for 42-DOF humanoid robot HRP-4C with ZMP delay [Reference Kajita112]; 3D LIPM-based 12-DOF model [Reference Kajita, Kanehiro, Kaneko, Yokoi and Hirukawa106]; algorithm for adopting 30% and 20% deviation in prescribed speed and step length respectively [Reference Dunn and Howe272]; moving horizon technique for inheritance of human walking behavior on the INRIA designed biped robot “BIP” [Reference Azevedo, Poignet and Espiau12]; versatile walk control framework by utilizing an ultrasonic reach sensor for straight upset pendulum-based biped robot “Meltran-II” [Reference Kajita and Tani104]; Poincare sections for asymptomatically stable periodic gait while regulating the impact of foot on the ground for an underactuated biped robot [Reference Grizzle, Abba and Plestan273]; horizontally composed plane having unknown step height for a biped mechanism made up of viscous elastomer [Reference Yamaguchi, Takanishi and Kato274]; a hybrid control consisting impedance control and CTC for swing leg and stance leg respectively with higher damping of leg while making contact with the ground [Reference Park and Chung275] and a robust adaptive controller inspired from “Turkey Walking” by virtual control for controlling speed, posture, and height [Reference Chew and Pratt276].

Furthermore, Pratt et al. [Reference Pratt, Chew, Torres, Dilworth and Pratt279] developed an algorithm virtually with intuitive natural dynamics and applied it on Spring Turkey and Spring Flamingo based on a 7-link planar biped robot having contact switches on the foot. Furthermore, Manchester et al. [Reference Manchester, Mettin, Iida and Tedrake179] designed a controller by first making a lower-dimensional arrangement of directions cross-over to the objective cycle and then utilizing a subsiding skyline input regulator to dramatically balance out the linearized elements of the cross-over states relevant to HZD system and obtained the gait of non-periodic trajectories and switching over rough and irregular terrains. Addedly, Iida and Tedrake [Reference Iida and Tedrake280] employed open-loop sinusoidal oscillation of hip actuator and developed a biped model of passive gait based on compass gait by changing the parameters of the oscillator.

Intelligence-based gait generation techniques have been employed to improve the biped gaits’ robustness on uneven terrain. In due course, Ma et al. [Reference Ma, Li and Qiao281] proposed hybrid intelligence methodology based on fuzzy NN controller and improved learning speed of any mobile robot to be controlled by itself on a real-time basis for sensing the direction of movement, target position by optical range finder and distances among various directions between obstacles with the help of ultrasonic sensors in an unknown environment. In addition to, Kanoulas et al. [Reference Kanoulas, Tsagarakis and Vona278] introduced a scheme for modeling, mapping, and tracking of rough rocky terrains for proper foot placement of robots on real-time data obtained from RGB-D and IMU sensor with the help of a set of parameterized patch models and bio-inspired sampling algorithms as shown in Fig. 14(a) and (b). The foot contacts are detected as bounded curved patches similar to foot support consisting of sparse seed point sampling, point cloud neighborhood search, and patch fitting and validation. The researchers also applied a 3D foothold perception architecture that utilizes the developed patch mapping and tracking scheme, as shown in Fig. 14(c). In general, the dynamically stable robots fail to walk on slippery terrain; the authors [Reference Chen and Goodwine282] suggest using moderate speed, short step lengths, and swing backward velocity. In addition to, Zamparelli et al. [Reference Zamparelli, Scianca, Lanari and Oriolo283, Reference Zamparelli, Scianca, Lanari and Oriolo284] generated online trajectories for CoM and ZMP by using the stability constraints with the help of an intrinsically stable MPC controller and applied it on the NAO, which is shown in Fig. 15. The presented problems collectively can be termed as the unknown environment, as demonstrated in the next section.

Fig. 14.

(a) Patches of various types and fits with noise range samples (blue) [Reference Kanoulas and Vona277], rock model mapping by an RGB-D Kinect sensor (right) [Reference Kanoulas, Tsagarakis and Vona278], (b) the principle of the homogeneous patch map [Reference Kanoulas, Tsagarakis and Vona278], (c) Human selected patches, in RGB-D recordings [Reference Kanoulas, Tsagarakis and Vona278].

Fig. 15.

Dynamic simulation of the NAO humanoid robot where red color represents the trajectory of the CoM (center of mass), and blue color represents the same trajectory without variation in vertical height (a) The NAO is stepping over the boxes of different heights, (b) The NAO walking on flat surface by lowering its CoM [Reference Zamparelli, Scianca, Lanari and Oriolo283, Reference Zamparelli, Scianca, Lanari and Oriolo284].

3.8. Gait generation in the unknown environment

When modeling and mapping the exact perspective of the unknown or uncertain environment, it becomes difficult for a biped robot to make a quick decision based on observational and sensory data collected by various sensors and devices. The robot must have a quick decision-making framework that makes it an intelligence-inbuilt mechanism. That is, more advanced technologies are required for doing so. Along with the decision policy, its controller also needs to perform the basic controlling operations for maintaining the dynamic balancing instantaneously. In comparing the various perspectives of intelligence in robotics and mechatronics, it can be said that animals are adaptable to their environments, and humans make some changes in the environment for comfort [Reference Fukuda and Arakawa285]. That means basic intelligence is all about being adaptive to the dynamic environment and making some improvements in the environment is advanced intelligence.

This section attempts to cover all perspectives and techniques proposed by various researchers around the globe in this direction. The bending of the knee joint at the lower hip position consumes more actuator torque. It was found that the minimum and maximum vertical distances between the ground and hip joint, and length of the shank and thigh greatly affect the torque [Reference Ding, Yang and Gan286, Reference Bian, Shao, Yang and Liang287]. The hip height has noble importance for stability, optimum actuator torques, preventing the link’s velocity discontinuities, and deriving the lower torso’s modified motion. Initially, a foot mechanism was configured by Yamaguchi et al. [Reference Yamaguchi, Kinoshita, Takanishi and Kato288] for two biped robots WAF-3 and WL-12RVIII, to evaluate the relative position of foot support concerning the landing surface and the inclination of the ground.

Many researchers have proposed RL and training modules for interpolating intelligence and intuitive inheritance in bipedal walking robots. Such as, Capi et al. [Reference Capi, Nasu, Barolli and Mitobe289] used the inherited data from human locomotion and implemented all learnings to the radial basis function neural network (RBFNN) algorithm to generate the real-time gaits by using a visual system for making an autonomous humanoid robot based on a minimum energy principle. The results obtained from the GA and RBFNN were verified and compared by simulation on the humanoid robot “Bonten-Maru I.” In addition to, the RL CPG actor-critic method learnt by policy gradient algorithm was implemented while introducing new schemes to the actor [Reference Nakamura, Mori, Sato and Ishii290]. Also, Pasandi et al. [Reference Pasandi, Dinale, Keshmiri and Pucci291] discussed a CPG encompassing a novel bounded output oscillatory coherent network. Here, each oscillatory mechanism configures one dimensional intermittent function as a stable limit cycle. The CPG access the online trajectories library and generates the trajectory in real-time for the iCub humanoid robot. Later on, Mousavi et al. [Reference Mousavi, Nataraj, Bagheri and Entezari292] and Bagheri et al. [Reference Bagheri and Mousavi293] developed a mathematical model to evaluate the path of the combined trajectory of a 7-DOF biped robot on different terrains. The effects of hip height on the torso’s modified motions and then applied third-order spline was applied due to high accuracy and precision for determining the inverse kinematic, dynamics, and control variables.

Similarly, Rioux and Suleiman [Reference Rioux and Suleiman294] conjointly presented an entire navigation framework for a humanoid robot by creating a map of the environment and setting some primitives as a base knowledge for loading weights and avoiding obstacles without any sensors. The researcher presented an efficient filtering procedure to enhance the performance of the SLAM algorithm and clear the field by removing the cart from the view. The approach experimented on the NAO humanoid robot having an RGB-D sensor. In addition to this, Luo et al. [Reference Luo295] developed a real-time terrain realization sensory system, as shown in Fig. 16, by confining the vital hardware to a microprocessor and a single sort of force sensor and also investigated the gait pattern performance by grouping the SVM (Support Vector Machine) algorithm. The authors observed that reinforcement learning,NN, CPG, mapping of the environment, and sensors-based systems had helped the researchers to make biped robots capable of walking in any unknown environment. Following that, the authors attempted to summarize the trends of previous research works discussed in Section 4.

Fig. 16.

(a) schematic diagram of hardware and configuration of robot and (b) transition phases between two distinct surfaces where A, B, and C represent smooth wood, smooth foam, and rough foam, respectively.