Hasan Eftun Orhon

Hasan Eftun Orhon

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.

H. Eftun Orhon, Caner Odabas, Ismail Uyanik et al.

Spring Loaded Inverted Pendulum (SLIP) model has a long history in describing running behavior in animals and humans as well as has been used as a design basis for robots capable of dynamic locomotion. Anchoring the SLIP for lossy physical systems resulted in newer models which are extended versions of original SLIP with viscous damping in the leg. However, such lossy models require an additional mechanism for pumping energy to the system to control the locomotion and to reach a limit-cycle. Some studies solved this problem by adding an actively controllable torque actuation at the hip joint and this actuation has been successively used in many robotic platforms, such as the popular RHex robot. However, hip torque actuation produces forces on the COM dominantly at forward direction with respect to ground, making height control challenging especially at slow speeds. The situation becomes more severe when the horizontal speed of the robot reaches zero, i.e. steady hoping without moving in horizontal direction, and the system reaches to singularity in which vertical degrees of freedom is completely lost. To this end, we propose an extension of the lossy SLIP model with a slider-crank mechanism, SLIP- SCM, that can generate a stable limit-cycle when the body is constrained to vertical direction. We propose an approximate analytical solution to the nonlinear system dynamics of SLIP- SCM model to characterize its behavior during the locomotion. Finally, we perform a fixed-point stability analysis on SLIP-SCM model using our approximate analytical solution and show that proposed model exhibits stable behavior in our range of interest.