Scalable closed-form trajectories for periodic and non-periodic human-like walking

We present a new framework to generate human-like lower-limb trajectories in periodic and non-periodic walking conditions. In our method, walking dynamics is encoded in 3LP, a linear simplified model composed of three pendulums to model falling, swing and torso balancing dynamics. To stabilize the motion, we use an optimal time-projecting controller which suggests new footstep locations. On top of gait generation and stabilization in the simplified space, we introduce a kinematic conversion method that synthesizes more human-like trajectories by combining geometric variables of the 3LP model adaptively. Without any tuning, numerical optimization or off-line data, our walking gaits are scalable with respect to body properties and gait parameters. We can change various parameters such as body mass and height, walking direction, speed, frequency, double support time, torso style, ground clearance and terrain inclination. We can also simulate the effect of constant external dragging forces or momentary perturbations. The proposed framework offers closed-form solutions in all the three stages which enable simulation speeds orders of magnitude faster than real time. This can be used for video games and animations on portable electronic devices with a limited power. It also gives insights for generation of more human-like walking gaits with humanoid robots.

Salman Faraji, Auke Ijspeert

We present a new framework to generate human-like lower-limb trajectories in periodic and non-periodic walking. In our method, walking dynamics is encoded in 3LP, a linear simplified model composed of three pendulums to simulate falling, swing, and torso balancing dynamics. To stabilize the motion, we use an optimal time-projecting controller which suggests new footstep locations. On top of gait generation and stabilization in the simplified space, we introduce a kinematic conversion that synthesizes more human-like trajectories by combining geometric variables of the 3LP model adaptively. Without any tuning, numerical optimization or off-line data, our walking gaits are scalable with respect to body properties and gait parameters. We can change body mass and height, walking direction, speed, frequency, double support time, torso style, ground clearance, and terrain inclinations. We can also simulate constant external dragging forces or momentary perturbations. The proposed framework offers closed-form solutions with simulation speeds orders of magnitude faster than real time. This can be used for video games and animations on portable electronic devices with limited power. It also gives insights for generation of more human-like walking gaits on humanoid robots.

2019

Scalable closed-form trajectories for periodic and non-periodic human-like walking

Salman Faraji, Auke Ijspeert

We present a new framework to generate humanlike lower-limb trajectories in periodic and non-periodic walking. In our method, walking dynamics is encoded in 3LP, a linear simplified model composed of three pendulums to simulate falling, swing, and torso balancing dynamics. To stabilize the motion, we use an optimal time-projecting controller which suggests new footstep locations. On top of gait generation and stabilization in the simplified space, we introduce a kinematic conversion that synthesizes more humanlike trajectories by combining geometric variables of the 3LP model adaptively. Without any tuning, numerical optimization or off-line data, our walking gaits are scalable with respect to body properties and gait parameters. We can change body mass and height, walking direction, speed, frequency, double support time, torso style, ground clearance, and terrain inclinations. We can also simulate constant external dragging forces or momentary perturbations. The proposed framework offers closed-form solutions with simulation speeds orders of magnitude faster than real time. This can be used for video games and animations on portable electronic devices with limited power. It also gives insights for generation of more human-like walking gaits on humanoid robots.

IEEE2019

Towards Robust Bipedal Locomotion

Salman Faraji

Thanks to better actuator technologies and control algorithms, humanoid robots to date can perform a wide range of locomotion activities outside lab environments. These robots face various control challenges like high dimensionality, contact switches during locomotion and a floating-base nature which makes them fall all the time. A rich set of sensory inputs and a high-bandwidth actuation are often needed to ensure fast and effective reactions to unforeseen conditions, e.g., terrain variations, external pushes, slippages, unknown payloads, etc. State of the art technologies today seem to provide such valuable hardware components. However, regarding software, there is plenty of room for improvement. Locomotion planning and control problems are often treated separately in conventional humanoid control algorithms. The control challenges mentioned above are probably the main reason for such separation. Here, planning refers to the process of finding consistent open-loop trajectories, which may take arbitrarily long computations off-line. Control, on the other hand, should be done very fast online to ensure stability. In this thesis, we want to link planning and control problems again and enable for online trajectory modification in a meaningful way. First, we propose a new way of describing robot geometries like molecules which breaks the complexity of conventional models. We use this technique and derive a planning algorithm that is fast enough to be used online for multi-contact motion planning. Similarly, we derive 3LP, a simplified linear three-mass model for bipedal walking, which offers orders of magnitude faster computations than full mechanical models. Next, we focus more on walking and use the 3LP model to formulate online control algorithms based on the foot-stepping strategy. The method is based on model predictive control, however, we also propose a faster controller with time-projection that demonstrates a close performance without numerical optimizations. We also deploy an efficient implementation of inverse dynamics together with advanced sensor fusion and actuator control algorithms to ensure a precise and compliant tracking of the simplified 3LP trajectories. Extensive simulations and hardware experiments on COMAN robot demonstrate effectiveness and strengths of our method. This thesis goes beyond humanoid walking applications. We further use the developed modeling tools to analyze and understand principles of human locomotion. Our 3LP model can describe the exchange of energy between human limbs in walking to some extent. We use this property to propose a metabolic-cost model of human walking which successfully describes trends in various conditions. The intrinsic power of the 3LP model to generate walking gaits in all these conditions makes it a handy solution for walking control and gait analysis, despite being yet a simplified model. To fill the reality gap, finally, we propose a kinematic conversion method that takes 3LP trajectories as input and generates more human-like postures. Using this method, the 3LP model, and the time-projecting controller, we introduce a graphical user interface in the end to simulate periodic and transient human-like walking conditions. We hope to use this combination in future to produce faster and more human-like walking gaits, possibly with more capable humanoid robots.

EPFL2018

Towards Robust Bipedal Locomotion

Salman Faraji

EPFL2018