The period-$1$ gait is a stable, efficient, and predictable walking pattern for bipedal robots, which is crucial for achieving precise control, energy optimization, and maintaining balance in complex environments. This study investigates the control of chaotic and multi-period gaits in a bipedal robot with impulsive actuation, focusing on the stabilization of such gaits into period-1 gaits and the expansion of their stable parameter regions. Three main contributions are presented: (1) stabilizing chaotic gaits to period-$1$ gaits using the Ott–Grebogi–Yorke (OGY) and bifurcation control methods; (2) converting multi-period gaits (e.g., period-$2$ and period-$4$) into period-$1$ gaits via bifurcation control; and (3) extending the stable parameter range of period-$1$ gaits by optimizing pulse thrust parameters. The bifurcation control method, though energy-intensive, proves more reliable than OGY method in preventing falls. Analytical and numerical results demonstrate that adjusting pulse thrust parameter $C$ significantly expands the stability domain, enhancing robustness against disturbances and parameter variations. The bifurcation control method proposed in this study is implemented via a constant thrust increment and validated through numerical simulations, which makes it easy to be applied in controller design. It provides both a theoretical foundation and a practical control scheme for achieving stable and efficient gait design in bipedal robots with impulsive actuation.

This paper investigates the influence of adding an upper body to a bipedal robot on its stable walking behavior. The robot’s parts are mutually interconnected through an actuator network system. Therefore, the movement pattern of the upper body depends on the type of interactions created with other limbs. Throughout the experiments, various interactions among the different body parts were tested. The results showed that a robot with a motionless upper body exhibited unstable walking behavior. However, once the same upper body was involved and interacted properly, with other body parts, its movement significantly helped to stabilize the behavior of the robot.

This paper proposes a shared control scheme which aims to achieve a stable control of the speed and turn of a bipedal robot during a delayed bilateral teleoperation. The strategy allows to get a delay-dependent damping value that must be injected to assure a bounded response of the hybrid system, while simultaneously, the human operator receives a force feedback that help him to decrease the synchronism error. Furthermore, a test where a human operator handles the walking of a simulated bipedal robot, to follow a curve path in front of varying time delay, is performed and analyzed.

This paper presents a whole-body dynamics controller for robust push recovery on a force-controlled bipedal robot. Featherstone's spatial vector method is used to deduce dynamics formulas. We reveal a relationship between the accelerations of the floating base and the desired external forces needed for those accelerations. Introducing constraints on the desired external forces causes corresponding constraints on the accelerations. Quadratic programming is applied to find the extremal accelerations, which recover the robot from pushes as best as possible. A robustness criterion is proposed based on the linear inverted pendulum model to evaluate the performance of push recovery methods quantitatively. We evaluate four typical push recovery methods and the results show that our method is more robust than these. The effectiveness of the proposed method is demonstrated by push recovery in simulations.

The problem of determining energy optimal walking motions for a bipedal walking robot is considered. A full dynamic model of a planar seven-link biped with feet is derived including the effects of impact of the feet with the ground. Motions of the hip and feet during a regular step are then modelled by 3rd order polynomials, the coefficients of which are obtained by numerically minimising an energy cost function. Results are given in the form of walking profiles and energy curves for the specific cases of motion over level ground, motion up and down an incline, and varying payload.

The paper is aimed at generating optimal swing motions during the single-support phase of sagittal gait. Unlike the previous Part 1 which deals with passive motions, all joints of the biped are assumed to be active in the present Part 2. The final conditions specify an impactless heel-touch in order to avoid a destabilizing effect on the biped motion. As the biped is essentially submitted to gravity forces, the motion is generated by minimizing the joint actuating torques. Feasible motions are defined by state inequality constraints limiting joint motions, and defining foot clearance and obstacle avoidance during the swing. The optimization problem is dealt with using Pontryagin's Maximum Principle. A final two-point boundary value problem is solved by implementing a shooting method. The approach presented is illustrated by various numerical simulations applying to a seven-body planar biped which has four or five active joints during the swing phase.

It has been shown that compass-like bipeds can walk passively by gravity-induced motion. Similarly, it has been stated that the unipodal phase of human gait may be regarded as a passive motion. This paper is aimed at determining precisely to what extent the swing phase of human-like walking can be considered as a non-actuated motion. More specifically, a method is developed that makes it possible to adjust initial conditions, step length and walk speed, as well as mass and inertia distribution of a bipedal robot, in order to generate a passive swing motion. The approach is demonstrated by using a 7-link planar biped. Numerical simulations show that purely passive unipodal transferring cannot be fully satisfactory. This approach is further considered in Part 2 of the paper which consists in computing optimal actuating joint torques to create perfectly feasible motions.

This paper deals with the decision mechanism analysis and the design of bipedal trajectories, for the stepping motion. For that we have used biomechanical model of the human body and dynamic control scheme previously developed by Gorce. We based our study on an experimental protocol, in order to determine behavioural laws for the task execution. We have developed a biped trajectory generation process, taking into account the biped height and the obstacle dimensions. Furthermore, we characterize the stepping motion feasibility by introducing a security notion, and we define an “Admissible control Domain”, which relies on the relative position of the biped to the obstacle and the obstacle dimensions. This domain definition has led us to define the biped behavioural strategies facing an obstacle: the biped executes the task at an accurate “chosen distance”, or stops or takes another way. Experimentations have allowed to validate simulations results.