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January 2019 - October 2022
The research concurrently started with my master thesis development under the supervision of professor G. Oriolo and professor L. Lanari and with the help of Dr. N. Scianca and Dr. V. Modugno. The problem of MPC dynamic gait generation in the presence of persistent disturbances (of any type, provided that they could be reasonably modeled as a force acting on the CoM) has been tackled. Persistent disturbances include mild perturbations that act on the robot, such as the effect of a weight that is being carried or a slope, or unmodeled dynamics. The idea was to endow the original Intrinsically Stable MPC scheme with robustness properties.
This phase of the research mainly dealt with the problem of generating stable gait trajectories i.e. ensuring no center of mass divergence with respect to the zero moment point, when persistent disturbances are present. In the case of limited in magnitude persistent disturbances, more intuitive approaches such as step position or timing adaptation can result in unnecessary motions or even in a loss of stability due to the integral action of an even small perturbation. To this purpose we assumed the footstep position to be fixed.
We achieved initial results by:
Making use of a disturbance observer and designing a proper stability constraint which embeds the disturbance information in the MPC. This idea is based on the consideration that the dynamic gait generation problem is anti-causal and a disturbance information (the whole disturbance evolution at each time) within a stability constraint allows to indirectly compensate the perturbation by anticipating its effect. Of course, an exact disturbance information is a rather strict requirement, thus a disturbance observer is a practical tool to for a causal implementation of the anti-causal problem.
Performing a support polygon restriction within the prediction horizon. This idea has been borrowed by the robust MPC literature and adapted to our case in order to guarantee recursive feasibility the proposed MPC scheme.
These results were published to 2019 International Conference on Humanoid Robots and 2020 International Conference on Robotics and Automation. The links to the manuscript pdf and the video material are available in the Publications page of this website.
The second phase of the research, conducted with Dr. N. Scianca and professors G. Oriolo and L. Lanari, dealt with the problem of timing adaptation in response to strong perturbations which are limited in time, allowing also the footstep positions to be modified. Thanks to a feasibility analysis of IS-MPC, it has been possible to design a step timing adapter as a simple linear quadratic program that modifies the current step timing in order to maintain the feasibility of IS-MPC when it would be lost for the action of a push. In this way, the IS-MPC scheme remains linear and increases its robustness properties against impulsive perturbations.
The result has been published to IEEE Robotics and Automation Letters, with the ICRA 2021 option.
We are now working on a holistic approach to combine all the proposed methods for a robust gait generation framework. An initial attempt in this direction has been presented at the 2020 I-RIM 3D conference (see the Publications page for a link to the paper ), however several questions remain open and are the object of on-going research: how to combine the use of the disturbance observer with the ZMP constraint restriction in order to formally ensure recursive feasibility of the scheme? Which is the best tradeoff between feasibility and recursive feasibility properties? How can the feasibility information be used for further improvements?
Drawback of robust locomotion research (personal comments)
Humanoid robots fall and research in robust locomotion makes them fall even more. This imply that they break.
The NAO v5 available at our lab was sent to the factory for repairs in march 2020.
Its right leg pitch joint broke several days after it came back from the repairs.
I personally had to repair it.
It actually broke again during further experiments.
Guess what? I had to go for 'home-repairs' again.
This time with much more confidence.
I ensure that no robot has been intentionally misused during this research.
Some inspiring works are listed below:
P.-B. Wieber, “Trajectory free linear model predictive control for stable walking in the presence of strong perturbations,” in 6th IEEE-RAS Int.Conf. on Humanoid Robots, 2006, pp. 137–14
L. Chisci, J. Rossiter, and G. Zappa, “Systems with persistent disturbances: Predictive control with restricted constraints,” Automatica,vol. 37, pp. 1019–1028, 2001
D. Mayne, M. Seron, and S. V. Raković, “Robust model predictive control of constrained linear system with bounded disturbances,” Automatica, vol. 41, pp. 219–224, 2005
N. A. Villa and P. Wieber, “Model predictive control of biped walking with bounded uncertainties,” in 17th IEEE-RAS Int. Conf. on Humanoid Robots, 2017, pp. 836–841
L. Lanari, S. Hutchinson, and L. Marchionni, “Boundedness issues in planning of locomotion trajectories for biped robots,” in 14th IEEE-RAS Int. Conf. on Humanoid Robots, 2014, pp. 951–958
D. J. Agravante, A. Sherikov, P. Wieber, A. Cherubini, and A. Kheddar, “Walking pattern generators designed for physical collaboration,” in 2016 IEEE Int. Conf. on Robotics and Automation, 2016, pp. 1573–1578
B. J. Stephens, “State estimation for force-controlled humanoid balance using simple models in the presence of modeling error,” in 2011 IEEE Int. Conf. on Robotics and Automation, 2011, pp. 3994–3999
L. Hawley and W. Suleiman, “External force observer for medium sized humanoid robots,” in 16th IEEE-RAS Int. Conf. on Humanoid Robots, 2016, pp. 366–371
H. Diedam, D. Dimitrov, P. Wieber, K. Mombaur, and M. Diehl, “Online walking gait generation with adaptive foot positioning through linear model predictive control,” in IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2008, pp. 1121–1126
N. Bohórquez and P. Wieber, “Adaptive step duration in biped walking: A robust approach to nonlinear constraints,” in 17th IEEE-RAS Int. Conf. on Humanoid Robots, 2017, pp. 724–729
S. Caron and Q. Pham, “When to make a step? Tackling the timing problem in multi-contact locomotion by TOPP-MPC,” in 17th IEEE-RAS Int. Conf. on Humanoid Robots, 2017, pp. 522–528
M. R. O. A. Maximo, C. H. C. Ribeiro, and R. J. M. Afonso, “Mixed-integer programming for automatic walking step duration,” in IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2016, pp. 5399–5404
M. Khadiv, A. Herzog, S. A. A. Moosavian, and L. Righetti, “Step timing adjustment: A step toward generating robust gaits,” in 16th IEEE-RAS Int. Conf. on Humanoid Robots, 2016, pp. 35–42
N. Scianca, D. De Simone, L. Lanari, and G. Oriolo, “MPC for humanoid gait generation: Stability and feasibility,” IEEE Transactions on Robotics, vol. 36, no. 4, pp. 1171–1188, 2020
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