Phd in THEORETICAL AND APPLIED MECHANICS

Thesis title: Legged robots: methods of optimal control and design

Nature has always been a source of inspiration for engineers and scientists who tried to replicate or mimick natural bio-mechanisms. In fact, this can be a smart strategy, since any natural living being is a highly optimized system over millions of years of evolution. Magnificent examples of engineering bio-inspired devices date from very ancient Magna Greece times, as the Archita’s dove automaton, and a large number of automata within the Erone’s tradition. The masterful Leonardo’s machines, such as the lion or the knight automaton, or the flying machines, some inspired by the flapping wings of birds, are also astonishing examples. Many engineers and robot designers assume the gait of animals is optimal since they would have been able to survive the competition and natural selection. For this reason, the quadruped robot tends to be designed inspired by the examples of nature. However, biological kinematics of locomotion is not reproducible directly by a legged robot, since biological muscles are extraordinarily efficient components, and animals can produce energy for their actuation by grabbing nutritive elements from the environment, transformed into actuation energy by a digestive process. This permits them to have a relatively light energy storage system. Moreover, artificial sensors are still inferior, in terms of number, miniaturization, and sensitivity against the ones owned by animals. Then interesting questions arise: is it possible to conceive more efficient quadrupeds than those proposed by nature? Is it possible to disclose a different kind of gaits for a quadrupedal mechanism as the product of a strict optimization process? This thesis investigates locomotion optimization methods, aimed at identifying optimal design choices for quadrupeds. Evolutionary algorithms, combined with the nonlinear programming, are used to generate gait parameters, a natural choice since they are based on evolutionary theory. In this phase, to avoid technological limitations, the process is independent of the leg structure or actuation. This allows the research to range over a wider set of solutions, thus recreating the mechanism of natural evolution. The study illustrates how to obtain locomotion solutions found in nature such as walking and galloping, showing how for a quadrupedal robot it is more convenient to walk at a lower speed and to trot at faster speed. A robot with the same size of a real horse is considered, and optimal solutions found by the algorithm are close to those selected by Nature. Finally, a nonlinear optimal control algorithm is used to track the optimal trajectories of the legs and body kinematics that, at low computational cost, permits to identify best performance gaits for any given speed of the robot’s body. A suitably developed obstacle avoidance technique, based on the velocity obstacle approach, shows remarkable results. Safe and unsafe regions of velocities are identified, the last leading with a high probability to crashes with other moving obstacles.