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Human stance in quiet mode, relies on feedback from eyes, skin, muscles and the inner ear and the control produced is a combination of strategies which enable a person to stay standing. This thesis presents the simulation and control of a hip actuated robotic model of human standing posture. / The first part of the thesis is devoted to recalling basic elements of the human balance system and to describe the balance strategies it uses to maintain an upright stance. Of the strategies presented, we consider the hip strategy which motivated the formulation of a hip actuated robot. An investigation into the control of nonlinear underactuated robots by linear controllers is done to verify the range and efficiency of the controlled system. / The second part of the thesis includes the investigation of two simplified models of the robot. Results using linear state feedback control are presented. The two models used are compared to clarify the use of one over the other. / We found that for linear controls, the size of the region of convergence decreased underactuated systems of increasing complexity. For our four degrees of freedom robot, the region of convergence is of 2.3 degrees for the actuated joints and of 1 degree for the unactuated joints. Our system is Lyapunov stable when the fully simplified model is assumed.

While the locomotion performance of legged robots over flat terrain or known obstacles has improved over the past few decades, they have yet to equal the performance of their animal counterparts over variable terrain. This work analyzes a multi-legged reduced order model of cockroach locomotion on variable slopes which will be used as an inspiration for a future sprawled posture legged robot. The cockroach is modeled as a point mass, and each leg of the cockroach is modeled as a massless, tangentially rigid, linearly elastic spring attached at the center of mass. All of the springs are actuated to allow changes in energy to the system. This is accomplished by varying the force free length of each leg in a feed-forward manner without reliance on feedback to change the actuation scheme. Fixed points of the model are found using a numerical solver that varies the velocity and phase shift parameters while leaving all other parameters at fixed values selected to match true cockroach motion. Each fixed point is checked for stability and robustness representing how effective the model is at staying on the predetermined gait, and transport cost as a measure of how efficient this gait is. Stable and robust fixed points were successfully found for the range of heading angles encompassing those of representative cockroach motion at each slope. Cockroaches may select the gait used based on stability or efficiency. Thus, additional fixed points were found in combination with a search routine that varies the leg actuation parameters in order to optimize either stability or metabolic efficiency, gaining insights into why cockroaches use the gaits that they do. Optimized fixed points were found based on four different leg functional combination families depending on whether each leg pushes or pulls. Optimized fixed point gaits exist for every incline slope studied between level ground and vertical slopes, at a range of initial heading angles that encompass those typically used by cockroaches. The selected gaits using both a stability based and an efficiency based optimization on the modeled cockroach are very similar. Both are also similar to gaits used by real cockroaches. The forces generated by the model are qualitatively similar to the experimental forces. / Graduation date: 2012

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