# Model-Based Identification and Control of a One-Legged Hopping Robot

## TL;DR

This paper develops and tests an approximate analytical model for a hip torque actuated dissipative SLIP on a one-legged hopping robot, enabling stable control and better understanding of natural locomotion.

## Contribution

It extends the TD-SLIP model with experimental validation on a real robot and designs a model-based controller for stable hopping behavior.

## Key findings

- The approximate analytical solution accurately predicts robot dynamics.
- The robot achieves stable hopping using the model-based controller.
- Torque-actuated models better approximate natural locomotion than traditional SLIP.

## Abstract

Spring-mass models are well established tools for the analysis and control of legged locomotion. Among the alternatives, spring-loaded inverted pendulum (SLIP) model has shown to be a very accurate descriptor of animal locomotion. Despite its wide use, the SLIP model includes non-integrable stance dynamics that prevent analytical solutions for its equations of motion. Fortunately, there are approximate analytical solutions for different SLIP variants. However, the practicality of such approximations are mostly tested on simulation studies with a few notable exceptions. This thesis extends upon a recent approximation to a hip torque actuated dissipative SLIP (TD-SLIP) model that uses torque actuation to compensate for energy losses. Systematic experiments for careful assessment of the predictive performance of the approximate analytical solution is presented on a well-instrumented one-legged hopping robot which is revised to enhance compatibility and accuracy of the system. Electronic structure of the robot is modified according to TD-SLIP model such that robot uses a real-time operating system to increase processing speed. Using the parameters and results generated by the predictive performance of the approximate analytical solution, a model-based controller is designed and implemented on the robot platform to generate a stable closed-loop running behaviour on the one legged hoping robot platform. In addition, ground reaction forces during the stance phase on the experimental platform is investigated and compared with the human running and the traditional SLIP model data to understand if torque-actuated models approximate natural locomotion better than traditional model.