In this project, I studied the quantitative impact of the variability in torque limits and variability in contact area in the ability of a robot to remain in balance.
This study builds on the concept of Balance Stability Boundary (BSB) is introduced in (Mummolo et al., 2017) and applied to a humanoid in more detail in (Mummolo et al., 2018). The BSB is an area in the Center of Mass (CoM) state-space that determines if a robot is in balance at any given time based on the current contact configuration. The BSB looks as shown below for a humanoid robot in single support (left) and double-support phase.
This is computed numerically by solving an optimization problem at many different CoM positions and looking for a feasible trajectory that brings the CoM to a statically stable position (e.g., the center of the feet). This renders the BSB numerically challenging to compute, so it is computed offline. What happens if we wanted to know what this BSB would have looked like if we had stronger motors, or larger feet, or a different contact configuration? One would need to recompute the corresponding BSB. Instead, in this project I show that one can use the Sensitivity Theorem from optimal control theory to iniexpensively compute an estimate of the BSB within small bounds of perturbing the torque or contact limits (Gonzalez et al., 2018). Below is what the BSB looks like as we increase the torque limits.
As the torque limits increase, the BSB grows until it reaches a point of saturartion, i.e., stronger motors will not make the robot more stable. This is because at this point the foot will start tipping and become more unstable.
I showed that it is possible to analytically determine when the BSB saturates under torque limit variation. In the case of variability of the area of the base of support, one can estimate when this saturation is reached.
References
2018
JMR
Contact-Dependent Balance Stability of Biped Robots
Carlotta Mummolo, William Z. Peng, Carlos Gonzalez, and 1 more author
@article{Mummolo2018,author={Mummolo, Carlotta and Peng, William Z. and Gonzalez, Carlos and Kim, Joo H.},title={Contact-Dependent Balance Stability of Biped Robots},journal={Journal of Mechanisms and Robotics},volume={10},number={2},pages={021009},year={2018},doi={10.1115/1.4038978},}
ASME-IDETC
Sensitivity of balancing in legged systems under torque constraint variations
Carlos Gonzalez, Carlotta Mummolo, and Joo H. Kim
In Proceedings of the ASME International Design Engineering Technical Conference, 2018
@inproceedings{Gonzalez2018ASME,author={Gonzalez, Carlos and Mummolo, Carlotta and Kim, Joo H.},title={Sensitivity of balancing in legged systems under torque constraint variations},booktitle={Proceedings of the {ASME} International Design Engineering Technical Conference},pages={1--9},year={2018},doi={10.1115/DETC2018-86063},}
2017
ASME-IDETC
Contact-Dependent Balance Stability of Walking Robots
Carlotta Mummolo, William Z. Peng, Carlos Gonzalez, and 1 more author
In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2017
@inproceedings{Mummolo2017ASME,author={Mummolo, Carlotta and Peng, William Z. and Gonzalez, Carlos and Kim, Joo H},title={Contact-Dependent Balance Stability of Walking Robots},booktitle={ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},pages={1--7},year={2017},doi={10.1115/DETC2017-68272},}
