Bayesian Programming

Probability as an extension of logic


Hierarchical Probabilistic Model of bipedal locomotion

PhD thesis of Raphaël Rose-Andrieux (2016)

Humanoid robots have always fascinated due to the vast possibilities they encompass. Indeed, a robot with the same sensorimotor features as a human could theoretically carry out the same tasks. However, a first obstacle in the development of these robots is the stability of a bipedal gait. Bipedal walkers are inherently unstable systems experiencing highly dynamic and uncertain situations. Uncertainty arises from many sources, including intrinsic limitations of a particular model of the world, the noise and perceptual limitations in a robot’s sensor measurements, and the internal mechanical imperfection of the system.

In this thesis, we focus on foot placement to control the position and velocity of the body’s center of mass. We start from a deterministic strategy, and develop a probabilistic strategy around it that includes uncertainties. A probability distribution can express simultaneously an estimation of a variable, and the uncertainty associated. We use a Bayesian model to define relevant variables and integrate them in the global frame.

Another benefit of this model is that our objective is also represented as a probability distribution. It can be used to express both a deterministic objective and the tolerance around it. Using this representation one can easily combine multiple objectives and adapt them to external constraints. Moreover, the output of the model is also a probabilistic distribution which fits well in a hierarchical context : the input comes from the level above and the output is given as objective to the lower level.

In this work, we will review multiple ways to keep balance and compare them to the results of a preliminary experiment done with humans. We will then extend one strategy to walking using foot placement to keep balance. Finally, we will develop a probabilistic model around that strategy and test it in simulation to measure its benefits in different contexts : integrating uncertainties, fusing multiple objectives and hierarchy.


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