Introduction

This library implements a series of algorithms generating CoM, ZMP and feet trajectories when given a set of foot-prints. In some cases, when a robot model provides a specialized inverse kinematics some algorithms can generate articular values.

Approach implemented

This code assumes that the mass distribution of your humanoid robot is centered around the waist. This is very important as all the algorithms implemented uses the single point mass model. If the masses of your robot legs and arms are too important to be ignored it is very likely that none of the algorithms will give a feasible pair of CoM-ZMP trajectories.

The first available algorithm is the preview algorithm Kajita2003 and Kajita2005. This algorithm is real-time if you do not change the foot-prints inside the preview window. If you do want to perform this modification you should see Morisawa2007. This come at the expense of a possible delay in the step execution, if the modifcations are too important. On the other hand this is one of the fastest solution to modify the futur in the stack of foot-steps.

Two variants similar to the preview control but including inequalities have been introduced by Wieber2006 and Dimitrov2009. The former takes 28 ms to be computed whereas the second introduce a new solver able to solve the problem in less than 2 ms. The solver named PLDP is included inside the library.

A new algorithm able to take a reference velocity of the CoM is also provided. Its description can be found in Herdt2010. This problem is currently solved using ql written by Pr. Schittkowski (Schittkowski2007 ). We thank him for letting us distribute his code in our LGPL code.

References

S. Kajita and F. Kanehiro and K. Kaneko and K. Fujiwara and K. Harada and K. Yokoi and H. Hirukawa, "Biped Walking Pattern Generation by using Preview Control of Zero-Moment Point", International Conference on Robotics And Automation, Taipei Taiwan, 2003

S. Kajita, Omsha, "Humanoid Robot", 2005,(In Japanese) ISBN4-274-20058-2, 2005

B. Verrelst and K. Yokoi and O. Stasse and H. Arisumi and B. Vanderborght, "Mobility of Humanoid Robots: Stepping over Large Obstacles Dynamically", International Conference on Mechatronics and Automation

M. Morisawa and K. Harada and S. Kajita and S. Nakaoka and K. Fujiwara and F. Kanehiro and K. Kaneko and H. Hirukawa, "Experimentation of Humanoid Walking Allowing Immediate Modification of Foot Place Based on Analytical Solution", IEEE Int. Conf. on Robotics and Automation, 3989–3994, 2007

P.-B. Wieber, "Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations" IEEE/RAS Int. Conf. on Humanoid Robots 137-142, 2006

D. Dimitrov, P.-B. Wieber, O. Stasse, H.J. Ferreau and H. Diedam, "An Optimized Linear Model Predictive Control Solver for Online Walking Motion Generation", IEEE International Conference on Robotics and Automation (ICRA) pp. 1171–1176, 2009

A. Herdt, D. Holger, P.B. Wieber, D. Dimitrov, K. Mombaur and D. Moritz "Online Walking Motion Generation with Automatic Foot Step Placement", Advanced Robotics Vol. 24 Issue 5-6, pp. 719–737

K. Schittkowski (2007): QL: A Fortran code for convex quadratic programming - user's guide, Report, Department of Computer Science, University of Bayreuth