Actuated Passive Dynamic Walker on Level Ground

While many walking robots demonstrate high levels of versatility, agility and stability, performance often comes at the cost of complicated controls and high energy use. A study of human gait patterns has shown that forward stride exhibits passive dynamics with minimal control. Subsequently, the energy required to power these passive dynamic walkers is greatly reduced. One passive dynamic walker, the rimless wheel model, depicts a regular polygon rolling along a flat surface. An oscillating inertia wheel provides natural control to minimize collisions between steps. Periodic and collisionless motion has been simulated under conditions with no energy losses. To compensate for energy losses, a motor adds torque between the frame and the inertial wheel. The goal of the presented research is to determine stable periodic and collisionless gait patterns across level ground of an inertia coupled rimless wheel with energy losses. The 2D system, composed of a frame, inertia wheel and drum, has been simulated in MATLAB based on the equations of motion. The frame is the only member that is in contact with the ground. The drum translates the oscillation of linear springs into radial motion of the inertia wheel while introducing the driving motor torque. During single stance, only one foot touches the ground and the system acts as an inverted pendulum. During double stance, two legs touch the ground and the frame is stationary. The moment produced by the inertia wheel propels the rimless wheel back into single stance. The ode45 function integrates the equations of motion and event detection is used to determine when to switch between single and double stance. The post-collision positions and velocities are calculated based on conditions before impact. Given appropriate values for physical parameters and initial conditions, the simulation obtains a solution to the non-linear equations of motion. Several tests of the simulation have been completed. When no actuation is present, total system energy is conserved in each phase of the motion. At impact, total energy always decreases. When a motor controller is used, system energy increases and decreases as the motor adds and absorbs energy. The current simulation demonstrates a single step based on initial conditions. This can be used to search for periodic and collisionless motion. After energy losses are introduced, a control method will be determined for actuating the system via the motor torque. Ultimately, the simulation is expected to result in solutions for the most efficient walking device across level ground.