There are two main categories of force control schemes: hybrid position-force control and impedance control. However, the former does not take into account the dynamic interaction between the robot's end effector and the environment. In contrast, impedance control includes regulation and stabilization of robot motion by creating a mathematical relationship between the interaction forces and the reference trajectories. It involves an energetic pair of a flow and an effort, instead of controlling a single position or a force. A mass-spring-damper impedance filter is generally used for safe interaction purposes. Tuning the parameters of the impedance filter is important and, if an unsuitable strategy is used, this can lead to unstable contact. Humans, however, have exceptionally effective control systems with advanced biological actuators. An individual can manipulate muscle stiffness to comply with the interaction forces. Accordingly, the parameters of the impedance filter should be time varying rather than value constant in order to match human behavior during interaction tasks. Therefore, this paper presents an overview of impedance control strategies including standard and extended control schemes. Standard controllers cover impedance and admittance architectures. Extended control schemes include admittance control with force tracking, variable impedance control, and impedance control of flexible joints. The categories of impedance control and their features and limitations are well introduced. Attention is paid to variable impedance control while considering the possible control schemes, the performance, stability, and the integration of constant compliant elements with the host robot.

Biped robots have gained much attention for decades. A variety of researches have been conducted to make them able to assist or even substitute for humans in performing special tasks. In addition, studying biped robots is important in order to understand human locomotion and to develop and improve control strategies for prosthetic and orthotic limbs. This paper discusses the main challenges encountered in the design of biped robots, such as modeling, stability and their walking patterns. The subject is difficult to deal with because the biped mechanism intervenes with mechanics, control, electronics and artificial intelligence. In this paper, we collect and introduce a systematic discussion of modeling, walking pattern generators and stability for a biped robot.

SUMMARYResearchers dream of developing autonomous humanoid robots which behave/walk like a human being. Biped robots, although complex, have the greatest potential for use in human-centred environments such as the home or office. Studying biped robots is also important for understanding human locomotion and improving control strategies for prosthetic and orthotic limbs. Control systems of humans walking in cluttered environments are complex, however, and may involve multiple local controllers and commands from the cerebellum. Although biped robots have been of interest over the last four decades, no unified stability/balance criterion adopted for stabilization of miscellaneous walking/running modes of biped robots has so far been available. The literature is scattered and it is difficult to construct a unified background for the balance strategies of biped motion. The zero-moment point (ZMP) criterion, however, is a conservative indicator of stabilized motion for a class of biped robots. Therefore, we offer a systematic presentation of multi-level balance controllers for stabilization and balance recovery of ZMP-based humanoid robots.

Currently, there is an intensive development of bipedal walking robots. The most known solutions are based on the use of the principles of human gait created in nature during evolution. Modernbipedal robots are also based on the locomotion manners of birds. This review presents the current state of the art of bipedal walking robots based on natural bipedal movements (human and bird) as well as on innovative synthetic solutions. Firstly, an overview of the scientific analysis of human gait is provided as a basis for the design of bipedal robots. The full human gait cycle that consists of two main phases is analysed and the attention is paid to the problem of balance and stability, especially in the single support phase when the bipedal movement is unstable. The influences of passive or active gait on energy demand are also discussed. Most studies are explored based on the zero moment. Furthermore, a review of the knowledge on the specific locomotor characteristics of birds, whose kinematics are derived from dinosaurs and provide them with both walking and running abilities, is presented. Secondly, many types of bipedal robot solutions are reviewed, which include nature-inspired robots (human-like and birdlike robots) and innovative robots using new heuristic, synthetic ideas for locomotion. Totally 45 robotic solutions are gathered by thebibliographic search method. Atlas was mentioned as one of the most perfect human-like robots, while the birdlike robot cases were Cassie and Digit. Innovative robots are presented, such asslider robot without knees, robots with rotating feet (3 and 4 degrees of freedom), and the hybrid robot Leo, which can walk on surfaces and fly. In particular, the paper describes in detail the robots’ propulsion systems (electric, hydraulic), the structure of the lower limb (serial, parallel, mixed mechanisms), the types and structures of control and sensor systems, and the energy efficiency of the robots. Terrain roughness recognition systems using different sensor systems based on light detection and ranging or multiple cameras are introduced. A comparison of performance, control and sensor systems, drive systems, and achievements of known human-like and birdlike robots is provided. Thirdly, for the first time, the review comments on the future of bipedal robots in relation to the concepts of conventional (natural bipedal) and synthetic unconventional gait. We critically assess and compare prospective directions for further research that involve the development of navigation systems, artificial intelligence, collaboration with humans, areas for the development of bipedal robot applications in everyday life, therapy, and industry.

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The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamicsbased control problem of complex robots. However, the regressor-based adaptive control used by VDC to control every subsystem and to estimate the unknown parameters demands specific knowledge about the system physics. Therefore, in this paper, we focus on reorganizing the equation of the VDC for a serial chain manipulator using the adaptive function approximation technique (FAT) without needing specific system physics. The dynamic matrices of the dynamic equation of every subsystem (e.g. link and joint) are approximated by orthogonal functions due to the minimum approximation errors produced. The control, the virtual stability of every subsystem and the stability of the entire robotic system are proved in this work. Then the computational complexity of the FAT is compared with the regressor-based approach. Despite the apparent advantage of the FAT in avoiding the regressor matrix, its computational complexity can result in difficulties in the implementation because of the representation of the dynamic matrices of the link subsystem by two large sparse matrices. In effect, the FAT-based adaptive VDC requires further work for improving the representation of the dynamic matrices of the target subsystem. Two case studies are simulated by Matlab/Simulink: a 2-R manipulator and a 6-DOF planar biped robot for verification purposes.

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The aim of this paper is to derive the equations of motion for biped robot during different walking phases using two wellknown formulations: Euler-Lagrange (E-L) and Newton-Euler (N-E) equations. The modeling problems of biped robots lie in their varying configurations during locomotion; they could be fully actuated during the single support phase (SSP) and overactuated during the double support phase (DSP). Therefore, first, the E-L equations of 6-link biped robot are described in some details for dynamic modeling during different walking phases with concentration on the DSP. Second, the detailed description of modified recursive Newton-Euler (N-E) formulation (which is very useful for modeling complex robotic system) is illustrated with a novel strategy for solution of the over-actuation/discontinuity problem. The derived equations of motion of the target biped for both formulations are suitable for control laws if the analyzer needs to deal with control problems. As expected, the N-E formulation is superior to the E-L concerning dealing with high degrees-offreedom (DoFs) robotic systems (larger than 6 DoFs).