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In the paper Learning Physical Parameters from Dynamic Scenes, 2018 a framework is presented to program a probabilistic physics engine for simulating the movements of a puck. A noisy-Newtonian dynamics was realized with a random generator which produces a near chaotic system. Each time, the simulation is started the movement is a bit different, but its not completely random. (It obeys to the physics engine.) What the authors have described is a parametrized stochastic intuitive simulator engine which is a great learning tool for transferring a domain into executable code. Such a mathematical model can be used by a hierarchical task network solver for figuring out the right interventions to bring the system into a goal state.

So my question is: The example with the puck is nice, but in the robotics domain we need something which can simulate a biped walker. How can I adapt the example into a naive physics engine for simulating the movements of a two-leg walking machine?

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program an “Intuitive Physics Engine" walking simulator? movements of a puck noisy-Newtonian dynamics was realized with a random generator produces a near chaotic system. not completely random obeys to the physics engine parametrized stochastic intuitive simulator engine great learning tool transferring a domain into executable code mathematical model used by a hierarchical task network solver right interventions to bring the system into a goal state

The example with the puck is nice, but in the robotics domain we need something which can simulate a biped walker.

How can I adapt the example into a naive physics engine for simulating the movements of a two-leg walking machine?


Artificial Pedal Mobility

Humans and many other biological organisms are naturally mobile through walking, running, jumping, and climbing and varieties and combinations of those. In mammals, these are subsets of a general coordinated mobility system relying heavily on four of the nine most commonly recognized senses.

  • Vision — both for orientation and for path and obstacle analysis
  • Tactile — to determine pressure on the feet
  • Proprioception — to determine pressure, stress, shear, and torque on mechanical components
  • Vestibular — both for orientation and delta rotation

The other five (taste, smell, hearing, radiography, and interoception) may be involved regarding where to move and how to do so safely but not directly in the coordination.

In bipeds and quadrupeds there are over 300 muscle controlled degrees of freedom (motive dimensions), over 100 of which are involved in mobility in a three dimensional world.

The conceptual distance between the puck coordination in Learning Physical Parameters from Dynamic Scenes and human walking simulation is like the conceptual distance between using an abacus at an ancient market and planning the astrophysics for a Mars launch, so the question is not easy to answer. Let's proceed nonetheless.

We can begin by looking at the features of the proposal in the MIT/Stamford U paper, Learning Physical Parameters from Dynamic Scenes, 2018, Tomer D. Ullman, Andreas Stuhlmüller, Noah D. Goodman, Joshua B. Tenenbaum.

Note that when the authors use the term, "representational framework," they are referring to a highly parameterized and thus generalized model through which a more practical robotics control model can be learned, but it is still a model. From here on, we shall call the generalized model they are proposing, "The Meta-model."

We should also be careful to distinguish the use of the term intuitive in its two contexts.

  • Physical coordination
  • Sensing paths through an intellectual maze without fully analyzing each option

The first of these two contexts is implied in the paper.

With these two distinctions clarified the features of the proposal are mainly these.

  • Learning mobility coordination
  • Leveraging a network of Bayesian inferences designed to infer multiple properties of multiple objects from a sequence of $f$ frames of a scene
  • Actions control generative subsystems
  • Vectors in $\mathbb{R}^n$ to "express the observable trajectories of objects in motion"
  • Meta-model that inherently models Newtonian relations between both intensive and extensive physical properties
  • Evaluation of heuristics through forming a rule from each heuristic and experimenting with the rule against the scene sequence
  • High probabilities of heuristics that lead to highly reliable rules, when developed at multiple levels of abstraction, is considered learning physics through experience (as opposed to learning in class after having learned the supporting concepts of language, science, and algebra)

Note that this proposal is not bipedal specific. It could apply to spiders, cats, Pogo sticks, and automated vehicles based on car wheel dynamics.

Differences Between Domains

The hockey puck, automated wheeled vehicle, and pedal domains are not the same.

  • Puck and wheeled vehicle domains are across two dimensional surfaces with relatively simple relations between puck and wheel dynamics and actual motion across the surface. Walking and the other pedal modes of mobility are largely in three space, however moving from $\mathbb{R}^2$ to $\mathbb{R}^3$ is not a prohibitive extension of the paper's proposal.
  • For the same reason, the movement of the puck is not much like the movement of joints in legs and feet. The trigonometric complexity is orders of magnitude higher in the pedal domain than that of the puck or wheeled vehicle. However cars and pucks can't run, jump, or climb, which limits their use in domains like nuclear power plant repair and terrain exploration.

Although the adaptation of the meta-model and learning approach proposed by Ullman et. al. is realistic, the idea that one person will do it is not. It will take a few decades of development across the AI robotics community to extend the ideas proposed to work with hips, knees, angles, and toes controlled by inputs from four of nine senses.

Also note that the Bayesian probabilistic approach to rule effectiveness likelihood is an extension of the earlier fuzzy logic approaches and is in fact formally the analysis portion of a fuzzy logic controller in two space.

The major shortcoming of the Ullman et. al. approach is the elimination of the robot (in this case the puck, hockey stick, and hockey player) from the learning experience. Even robotic control of the hockey stick using a long robotics arm would change the game considerably and make it more practical. Humans (and dogs and spiders) do not learn physics and then apply it in motive control of their limbs. They learn to walk and then learn the rules that explain the walking twenty years later, if they specialize in mobility mechanics at a university.

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