Model based methods for the control and planning of running robots

Abstract

The Spring-Loaded Inverted Pendulum (SLIP) model has long been established as an effective and accurate descriptive model for running animals of widely differing sizes and morphologies. Not surprisingly, the ability of such a simple spring-mass model to capture the essence of running motivated several hopping robot designs as well as the use of the SLIP model as a control target for more complex legged robot morphologies. Further research on the SLIP model led to the discovery of several analytic approximations to its normally nonintegrable dynamics. However, these approximations mostly focus on steady-state running with symmetric trajectories due to their linearization of gravitational effects, an assumption that is quickly violated for locomotion on more complex terrain wherein transient, non-symmetric trajectories dominate. In the first part of the thesis , we introduce a novel gravity correction scheme that extends on one of the more recent analytic approximations to the SLIP dynamics and achieves good accuracy even for highly non-symmetric trajectories. Our approach is based on incorporating the total effect of gravity on the angular momentum throughout a single stance phase and allows us to preserve the analytic simplicity of the approximation to support research on reactive footstep planning for dynamiclegged locomotion. We compare the performance of our method with two other existing analytic approximations by simulation and show that it outperforms them for most physically realistic non-symmetric SLIP trajectories while maintaining the same accuracy for symmetric trajectories. Additionally, this part of the thesis continues with analytical approximations for tunable stiffness control of the SLIP model and their motion prediction performance analysis. Similarly, we show performance improvement for the variable stiffness approximation with gravity correction method. Besides this, we illustrate a possible usage of approximate stance maps for the controlling of the SLIP model. Furthermore, the main driving force behind research on legged robots has always been their potential for high performance locomotion on rough terrain and the outdoors. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments (e.g flat ground), or rely on kinematic planning with very low speeds. Moreover, the traditional separation of planning from control often has negative impact on the robustness of the system against model uncertainty and environment noise. In the second part of the thesis, we introduce a new method for dynamic, fully reactive footstep planning for a simplified planar spring-mass hopper, a frequently used dynamic model for running behaviors. Our approach is based on a careful characterization of the model dynamics and an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a very large, nearly global domain of attraction that requires no explicit replanning during execution. Finally, we use a simplified hopper in simulation to illustrate the performance of the planner under different rough terrain scenarios and show that it is robust to both model uncertainty and measurement noise.