This paper addresses robust landing stabilization in humanoid locomotion on uneven terrain. The core idea is to find a configuration of the robot that results in small impulsive force when an unexpected obstacle is encountered, and to adjust post-contact reference for swing foot with which the pose of the foot is stabilized on the obstacle. This can be achieved by walking with heel strike motion (validated by the impact map analysis) and by employing hybrid admittance control combining the admittance control with reset of post-contact reference, embedded into the momentum-based whole-body control framework. The validity of the proposed algorithm is verified by simulation with a physics engine.

This paper addresses the balance recovery problem for biped robots in the sagittal plane, affected by an instantaneous push. It is particularly seen that, when future footsteps of the robot should be re-generated to deal with a strong push, taking the foot size into account significantly reduces the number of footsteps required for the balance recovery. As an illustration of this idea, we generalize the so-called reactive step generator in the authors' previous work, by employing variation of the zero-moment point inside the supporting region as an additional control input for stabilization of divergent component of motion. On the basis of a mathematical formulation of the balance recovery problem, we verify the validity of the proposed algorithm with both theoretical and simulation results.

This paper addresses reactive generation of step time and location of biped robots for balance recovery against a severe push. Key idea is to reformulate the balance recovery problem into a tracking problem for "hybrid" inverted pendulum model of the biped, where taking a new step implicitly yields a discrete jump of the tracking error. This interpretation offers a Lyapunov-based approach to reactive step generation, which is possibly more intuitive and easier to analyze than large-scaled or nonlinear optimization-based approaches. With the continuous error dynamics for the divergent component of motion (DCM), our strategy for step generation is to decrease the "post-step" Lyapunov level for DCM error at each walking cycle, until it eventually becomes smaller than a threshold so that no more footstep needs to be adjusted. We show that implementation of this idea while obeying physical constraints can be done by employing a hybrid tracking controller (together with a reference model) as our reactive step generator, consisting of a simple DCM-based continuous controller and a small-sized quadratic programming-based discrete controller. The validity of the proposed scheme is verified by simulation results.

In this paper, we address the problem of generating a trajectory of the zero-moment point (ZMP) and the rate of angular momentum for a bipedal robot in the sagittal plane, with which the balance of the robot is recovered from external push. Unlike most previous works that adjusted a pre-designed ZMP or solved (possibly too heavy) nonlinear optimization problems, our main purpose is to develop a fully reactive step generator in the sense that (a) no pre-calculation of nominal trajectory is required, and (b) the algorithm is simple enough to operate in real time, only by utilizing the current state of the robot. For the design, it is seen by reinterpreting the centroidal dynamics in the hybrid model framework that the balance recovery problem can be recast as the problem of stabilizing a hybrid-type (linear) inverted pendulum model. On the basis of the concept of the divergent component of motion, a simple hybrid control law is then constructed to stabilize the hybrid system, which serves as a step generator that automatically determines where and when to step. This paper briefly sketches a mathematical proof on the performance of the proposed generator from a control-theoretic perspective, which is also supported by simulation results.