Inverse Kinematics

I recently signed up for an IEEE membership, which got me access to a few select journals, namely the IEEE Transactions on Robotics. Every now and then I go back and check out what new articles have been posted, and I thought I'd share one.

Sugihara, T. "Solvability-Unconcerned Inverse Kinematics by the Levenberg--Marquardt Method"

This is a very practical paper that compares a number of IK algorithms, providing a brief overview of each. For robot systems such as humanoids, we are always concerned with two problems: resolving redundancy and overcoming numerical instability due to singular matrices. This paper addresses the problem of numerical stability and speed. I highly recommend it to anyone studying such problems.

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Push Recovery While Walking in Place Experiments

Today I took some video of my current work on push recovery while walking in place. In this experiment, the humanoid robot is walking in place using a model predictive controller (MPC) that continuously optimizes footsteps and center of mass (COM) motion. The MPC outputs desired footstep locations and center of pressure location (COP) which are converted to desired torques for the full body using multi-objective inverse dynamics.

Hip Strategy Experiments

I took some video yesterday demonstrating new robot balance control that can perform a "hip strategy". Basically there are multiple objectives, one to keep the center of mass (COM) over the feet and another to keep the torso upright. Keeping the COM over the feet is more important, so after a large push the robot will decide to swing its torso forward to achieve that objective. Once it is stabilized, it can return to an upright posture. The video demonstrates pushing from both directions in the sagittal plane which is the more unstable direction.

The basic controller is similar to the one used in [1], which uses optimization to trade off between several objectives related to balance. In this case, there are objectives related to regulating the COM, regulating posture, regulating angular momentum, and minimizing joint torques and contact forces. Inequality constraints are imposed to keep the feet flat on the ground and avoid joint torque limits. This is a very generalizable and easy to implement approach to full body balance control.

[1] Y. Abe, M. da Silva, and J. Popovic, “Multiobjective control with frictional contacts,” Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation, 2007, pp. 249-258.