In this paper, we present a novel control strategy for running of bipedal robots with compliant legs. To achieve this goal and to take advantage of the characteristics of the template, we match the dynamics of the full multibody model of a real biped robot with the dynamics of a well-known running template called spring loaded inverted pendulum (SLIP) model. This can be viewed as a template and anchor approach. Because the SLIP model is theoretically conservative, it always operates at a constant energy level. However, real robots operate at various energy levels due to the positive and/or negative work done by the motors, inherent damping/friction of the components and more importantly, the regular ground impact that occurs during the running process. As a case study the proposed controller was implemented on a simulation of the bipedal robot called ATRIAS. The full dynamic equations for running of the ATRIAS robot are derived using the Lagrangian approach. To make our multibody biped robot run with a steady and stable gait that tracks the SLIP model dynamics, a two-level controller is proposed. The upper level controller in stance phase is designed with feedback linearization to make the active SLIP model follow the SLIP model trajectory. The lower level controller in stance phase is designed for the multibody model to track the toe force profile of the active SLIP model. Two active SLIP architectures are proposed for locked and unlocked torso cases of the robot. Simulation results demonstrate stable running based on this strategy for both cases of the ATRIAS model with locked and unlocked torso angle. Matching the SLIP dynamics on running biped robots not designed for spring-mass gaits is impossible due to actuator limitations, or, at best, inefficient.

This paper investigates two fundamental structures for biped robots and a control strategy to achieve stable biped running. The first biped structure contains straight legs with telescopic springs, and the second one contains knees with compliant elements in parallel with the motors. With both configurations we can use a standard linear discrete-time state-feedback control strategy to achieve an active periodic stable biped running gait, using the Poincare map of one complete step to produce the discrete-time model. In this case, the Poincare map describes an open-loop system with an unstable equilibrium, requiring a closedloop control for stabilization. The discretization contains a stance phase, a flight phase and a touch-down. In the first approach, the control signals remain constant during each phase, while in the second approach both phases are discretized into a number of constant-torque intervals, so that its formulation can be applied easily to stabilize any active biped running gait. Simulation results with both the straight-legged and the kneed biped model demonstrate stable gaits on both horizontal and inclined surfaces.

This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles.