Trajectory Planning for the Walking Biped

A real-time joint trajectory generator for planar walking bipeds is proposed. In the near future this trajectory planner will be implemented on the robot “Lucy”, which is actuated by pleated pneumatic artificial muscles. The trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the strategy developed is demonstrated by simulation results. A first simulation is performed under the assumption of perfect tracking by the controllers of the different actuators. This allows one to verify the effectiveness of the trajectory planner and to evaluate the postural stability. A second simulation is performed while taking the control architecture of the real robot into account. In order to have a more realistic simulation the proposed control architecture is evaluated with a full hybrid dynamic simulation model of the biped “Lucy”. This simulator combines the dynamical behaviour of the robot with the thermodynamical effects that take place in the muscle-valves actuation system. The observed hardware limitations ∗Supported by the Fund for Scientific Research Flanders (Belgium) The International Journal of Robotics Research Vol. 25, No. 9, September 2006, pp. 867-887 DOI: 10.1177/0278364906069343 ©2006 SAGE Publications of the real robot and expected model errors are taken into account in order to give a realistic qualitative evaluation of the control performance and to test the robustness. KEYWORDS—walking biped, real-time trajectory planning, natural dynamics, angular momentum, objective locomotion parameters