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# Humanoid Push Recovery: Use of simple models and learning

Much of this work was a collaboration with Dr. Jerry Pratt at the Institute of Human and Machine Cognition, Pensacola, Florida.
 For large magnitude pushes a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards When and where to take a step" has not yet emerged. Towards this goal, we present the concept of Capture Point, the point on the ground where a humanoid must step to in order to come to a complete stop. As the push force progressively grows larger, balance strategies that are used include moving the Center of Pressure within the foot, utlizing angular momentum through lunging and windmilling'' of appendages, and eventually taking a step. The location of the Capture Point relative to the base of support determines which strategy the robot should adopt to successfully stop in a given situation. Computing the Capture Point for a humanoid, in general, is very difficult or too complex to be practical. However, using the well-known linear inverted pendulum model, we can compute exact analytical solutions of the Capture Point. Note that the linear inverted pendulum model is a significant approximation of the robot dynamics (more on this below), but the capture point calculation is exact from this approximate model. Time elapsed image sequence showing the simulated twelve degree-of-freedom robot recover from a forward push by taking a step. Snapshots are left to right, top to bottom, spaced at 0.2second increments. The robot is impulsively pushed, with a force of 300N for 0.1seconds, corresponding to a velocity change of 1.2ms. The robot takes a step to a Capture Point to recover balance. Time elapsed image sequence showing the simulated twelve degree-of-freedom robot recover from a diagonal push by taking a step. Snapshots are left to right, top to bottom, spaced at 0.2second increments. The robot is impulsively pushed, with a force of 200N for 0.1seconds, corresponding to a velocity change of 0.8ms. The robot takes a step to a Capture Point to recover balance. Time elapsed image sequence showing the simulated twelve degree-of-freedom robot recover from a push by lunging. Snapshots are left to right, top to bottom, spaced at 0.1second increments. The robot is impulsively pushed, with a force of 160N for 0.05seconds, corresponding to a velocity change of 0.32ms. The robot lunges to recover balance, without taking a step. We extend the linear inverted pendulum model to include a flywheel body and compute exact solutions of the Capture Point for this model. Adding this rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do. We demonstrate that the Capture Region is significantly enlarged by using the reserve angular momentum. Training the robot to improve its performance: While simple dynamic models are useful for fast computation, model assumptions and modeling errors lead to stepping in the wrong place and resulting in large velocity errors after stepping. To address this we have two major options. One approach is to use complex models that are more faithful representation of the true dynamics of the robot. While this is a reasonable approach, in reality, complex models require significantly more computing power, sometimes cutting back the advantage gained in improving the model. From observation of push recovery behavior of human, we contend that recovery from a disturbance should not require sophisticated modeling, accurate physical parameter measurements, or overly constraining limitations on the walking control system. With this philosophy we adopt a different approach where we decide to preserve the analytical solution of the simple linear inverted pendulum model. In order to compensate for the model deficiency we turn to soft-computing based learning techniques. Using learning techniques we update the analytically predicted Capture Points. Diagram shows results of stepping to various locations for a given push. Pink circles show Capture Points. At other points a red arrow shows the resulting vector from the new support foot to the CoM position and a green arrow shows the resulting CoM velocity at the point where the CoM comes closest to the center of the support ankle. The black and white target shows the ground projection of the CoM when the Desired Step Location Calculator was queried. The blue rectangle shows the location of the current stance foot. The center of the grid of points is the location of the predicted Capture Point using the Linear Inverted Pendulum Model. Stopping Error using Capture Points predicted from the Linear Inverted Pendulum Model (left) and adding a Capture Point offset predicted from the simple curve fit based on the CoM velocity angle at the decision event(right). Nine different force impulses were applied from 20 directions. The mean Stopping Error when using the Linear Inverted Pendulum model is 0.137J/kg, with a stopping success rate of 1 out of 180 trials. The mean squared error when using the curve fit to predict Capture Point offsets is 0.0192 J/kg, with a success rate of 45 out of 180 trials. Results of on-line learning. A successful trial has a value of 1, and a failed trial has a value of 0, regardless of the residual Energy Error. The points plotted represent the average value over 200 trials. The filtered estimate was found by using a forward/reverse 500 trial running average of the data padded on either side with the average of the first and last 500 iterations. The vertical lines represent training being turned on at 1000 iterations and off after 3000 iterations. The disturbance forcs used to test the controller before and after training are identical. This approach makes a vast improvement to the push recovery ability of the robot while continuing to be fast. We validate the results on a three dimensional humanoid robot simulation with 12 actuated lower body degrees of freedom, distributed mass, and articulated limbs. Using our learning approach, robustness to pushes is significantly improved as compared to using the linear inverted pendulum model without learning.

A list of my papers on this topic:

• S.-K. Yun and A. Goswami,
Momentum-Based Reactive Stepping Controller on Level and Non-level Ground for Humanoid Robot Push Recovery, IROS 2011, San Francisco, CA, September 2011.

(pdf).

Abstract: This paper presents a momentum-based reactive stepping controller for humanoid robot push recovery. By properly regulating combinations of linear and angular momenta, the controller can selectively encourage the robot to recover its balance with or without taking a step. A reference stepping location is computed by modeling the humanoid as a passive rimless wheel with two spokes such that stepping on the location leads to a complete stop of the wheel at the vertically upright position. In contrast to most reference points for stepping based on pendulum models such as the {\em capture point}, our reference point exists on both level and non-level grounds. Moreover, in contrast with continuously evolving step locations, our step location is stationary. The computation of the location of the reference point also generates the duration of step which can be used for designing a stepping trajectory. Momentum-based stepping for push recovery is implemented in simulations of a full size humanoid on 3D non-level ground.

Animations:
Robot stepping on level ground,upward and downward slopes

• J. Rebula, J. Pratt, F Canas and A. Goswami,
Learning Capture Point for Improved Humanoid Push Recovery,
Humanoids07, Pittsburgh, PA, November-December 2007.

(pdf).

Abstract: We present a method for learning Capture Points for humanoid push recovery. A Capture Point is a point on the ground to which the biped can step and stop without requiring another step. Being able to predict the location of such points is very useful for recovery from significant disturbances, such as after being pushed. While dynamic models can be used to compute Capture Points, model assumptions and modeling errors can lead to stepping in the wrong place, which can result in large velocity errors after stepping.We present a method for computing Capture Points by learning offsets to the Capture Points predicted by the Linear Inverted Pendulum Model, which assumes a point mass biped with constant Center of Mass height. We validate our method on a three dimensional humanoid robot simulation with 12 actuated lower body degrees of freedom, distributed mass, and articulated limbs. Using our learning approach, robustness to pushes is significantly improved as compared to using the Linear Inverted Pendulum Model without learning.

Robot performance before learning
Robot performance after learning

• J. Pratt, J. Carff, S. Drakunov and A. Goswami,
Capture Point: A Step toward Humanoid Push Recovery,
Humanoids2006, Genoa, Italy, December 2006.

(pdf).

Abstract: It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards “When and where to take a step” has not yet emerged. Towards this goal, we present methods for computing Capture Points and the Capture Region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the Capture Region and the Base of Support determines which strategy the robot should adopt to successfully stop in a given situation.

Computing the Capture Region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the Capture Region is simplified. We extend the wellknown Linear Inverted Pendulum Model to include a flywheel body and show how to compute exact solutions of the Capture Region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the Capture Region.

We present simulations of a simple planar biped that can recover balance after a push by stepping to the Capture Region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass.