Optimization and Control of Dynamic Humanoid Running and Jumping

Animals in nature display a nearly seamless capability to navigate the world around them. Whether running up a steep mountain trail, weaving through a dense forest, or jumping to clear obstacles, legged animals are capable to dynamically negotiate challenging terrains with grace and efficiency. The development of legged machines with even a portion of this legged mobility would provide great benefit to applications in defense, search and rescue, and planetary exploration. The objective of this dissertation is to make a significant contribution towards the dynamic capabilities of legged machines, more specifically as applied to humanoid robots. Humanoid robots represent one potential platform to study legged mobility. Compared to other legged morphologies, humanoids have increased potential for application in human-inhabited environments due to their structural similarity to humans. Despite the surge of work on humanoid robotics in the recent decade, current machines are not yet capable of any significant dynamic mobility. The development of control systems for dynamic humanoids is a difficult task given their high number of degrees of freedom, which require continuous coordination, as well as their complex nonlinear dynamics, which change fundamentally in the presence of contacts with the ground. Performance of dynamic movements is further complicated by frequent periods of static instability, requiring continuous motion to prevent a catastrophic fall. Even for a basic dynamic movement, such as a high-speed run, current approaches ii تیاس ب لتم Mat ab Si e.c MatlabSite.com تیاس بلتم for humanoids are unable to generalize to a range of speeds or turning rates, or have not demonstrated robustness to disturbances. With the control approach described in this dissertation, a standing long jump, high-speed run, running turn, and running long jump are demonstrated in 3D dynamic simulation with a 26 degree of freedom (DoF) humanoid model. By focusing on the design and control of the salient features of the dynamic movements, the system is capable to run at speeds of up to 6.5 m/s, which is comparable to the speed of an Olympian in the 5000m race. Advances in whole-body humanoid task-space control are presented, where the control of centroidal momentum is shown to be an enabling approach for dynamic balance control. This approach is shown to result in emergent upper-body motions to maintain balance in a number of examples. New relationships between the dynamics of centroidal momentum and the dynamics of the humanoid in joint-space are highlighted, which will simplify future application of this emerging approach. Algorithms to compute the task-space inertia matrix and a formulation of the task-space control problem as a conic optimization problem, presented here, provide computational benefits to applications of task-space control. Further, these advances enable all the control examples for the 26 DoF humanoid model used here to be performed at real-time rates. A high-level running controller based on a 3D-SLIP model is presented to interface with this whole-body controller, resulting in automatic footstep planning to maintain balance across a range of speeds in the face of disturbances. The controller is also shown to be general to produce high-speed running turns. For instance, when running at 3.5 m/s the humanoid is capable to execute a tight turn with a radius that is approximately 1/4 that of a 400m track. Through extensions of the 3D-SLIP iii تیاس ب لتم Matl Sit .c MatlabSite.com تیاس بلتم model, this framework is also shown to be general to produce a running long jump, an aperiodic movement which includes significant underactuated periods of flight. The trajectory optimization approach for this model is shown to result in long-jump strategies that match those employed in human long jumpers, and highlights the importance of takeoff-velocity angle. Rather than employing the ballistic optimum of a 45◦ takeoff-velocity angle, the approach matches biological findings which use a more shallow angle to maximize jump span. iv تیاس ب لتم Matlab Site.com MatlabSite.com تیاس بلتم