| It may seem preposterous, but walking is actually faster than rolling under certain conditions. Even though bio-inspired robots can have advantageous mobility, they can also be very inefficient. This idea, the balance between efficiency and speed, is the core of this dissertation. Inefficiencies in legged robotics are due to many things, e.g., collision losses, joint friction, etc., but here we address the inefficiencies due to suboptimal control schemes.;We seek a control scheme that will decide: 1) whether it makes sense to walk or not—we seek an energy regime for walking that depends on the energy already in the system, and then 2) how wide we should make our stride, i.e., the optimal stride angle, and finally 3) an optimal switching curve: when should we power, and when should we coast to achieve the greatest possible speed at the least energy cost.;This dissertation presents control schemes for a lossless "rimless wheel" model as well as a two-link serial robot model for walking. Using Pontryagin's Maximum Principle (PMP), we describe the cost function, the state/co-state equations, and the switching conditions for these models. The research results of both models show an "on-off' control and the "switching curve" between these control extremes. It is not possible to find a complete closed-form solution for some parts of this problem, and numerical methods, such as dynamic programming and Nelder Mead optimization, must be used for simulation and visualization of the results. |
