The objective of this study is to propose control strategies for legged robots to walk and run naturally like humans and animals. To achieve this goal, we use the spring-mass model for the legged robots to be able to create the same dynamics in the leg as humans and animals. In this way, understanding the natural dynamics of the system plays the central role and the strategy is to manipulate the dynamics of the system in the favor of final goals. This research elaborates to follow the template-anchor-robot notion, therefore the process starts with reduced order model (template) and then shows the validity of the control policy on the full order model (anchor) and finally implements the policy on the robot.
The study starts with analyzing the dynamics of the bipedal spring-mass model to find the workspace and the possible limit cycles in each energy level. After that, a deadbeat control strategy is proposed to pinpoint the system to the desired limit cycle. It is shown that two steps are necessary and sufficient for the deadbeat control but it turned out that the sensitivity of the system to the touch-down angle is a challenging issue for implementing on real robots. Therefore, unlike the deadbeat control technique that pinpoints the system to the desired states, four swing leg control policies are proposed to gradually approach the desired limit cycles. The large basins of attraction of these proposed control policies show that the system can be reliably controlled to the desired gaits after large perturbations. The implementation on the full order model of the robot as well as the robot itself confirms this conclusion. Furthermore, a time-based feed-forward control strategy for the stance phase of the bipedal spring-mass model is combined with one of the proposed swing leg control policies to stabilize the model and manages the energy of the system. The simulations show that this technique can stabilize the model and manages the energy level of the system and the rate of convergence would be higher for spring-mass system with some damping in parallel to the spring. By implementing this policy on the full order model of the robot, stable walking gaits, as were predicted by the reduced order model, were obtained. Finally, a flight phase control policy is proposed for spring-mass running robots through investigating birds' running experiments. In this control policy, three objective functions were considered to fulfill safety and efficiency during running. It turned out that with a simple swing leg policy (constant leg angular acceleration), both goals of damage avoidance and energy efficiency can be fulfilled at once.