Time-scaling Control of a Compass Type Biped Robot

This paper presents a robust control strategy driving an actuated compass gait robot towards steady and periodic gaits. By robust we mean a large basin of attraction for the limit cycle. The originality lies in the generation of the swing leg reference angle and speed as a simple function of the supporting leg angle. Simulations and experimentation with a prototype showed that the system exhibits asymptotically stable walking cycles with large and strong basins of attraction. 1 INTRODUTION Investigations involving biped robots are usually done with one the following goals in mind: creating a complementary tool to clinical studies for the understanding of human walking mechanisms or paving the way for future robotic developments in various emerging fields. Either way, the complexity of the bipedal gait remains an obstacle to its understanding and explains why searchers in the field spend years understanding its subtleties. The compass gait, as described by Goswani et al. [1] and Garcia, Ruina and al [2] is widely accepted as the simplest model of bipedal locomotion and is also recognized, by the biomechanists, as the most basic sub-action that explain the overall walking mechanism. This simplicity allows much insight into the dynamics and control of the human gait and the drawing of strong foundations for the future development of more complex walkers. Furthermore, this gait being dynamic, the kinetic energy is partly transferred from one step to the other, permitting energy efficiency which, according to a general feeling, will be a major obstacle to the implementation of walking robots in the everyday life. McGeer [3] and many others already demonstrated the possibility of near passive gaits. The goal of this study was to create the simplest dynamic biped robot walking on a level ground with a stable and periodic limit cycle and an attractor large and strong enough to recover quickly after a perturbation. Furthermore, it was required that the robot’s behaviour take advantage of the natural interaction of the gravitational field with kinetic and potential energy to give it a smooth, efficient and natural-like walking pattern. This paper presents both simulation and experimentation results of a simple controller ensuring a large basin of attraction in order to reach a dynamically stable walking mode without any complex planning of the trajectory. 2 Dynamic modelling of the compass gait The chosen model, shown at figure 1, walks with a compass gait similar to the one described by many authors [1-3] with the important distinction that it doesn’t use an incline plane as an energy source. Rather, in order to recover from energy losses due to friction and impacts or to modify the walking cycle frequency, torque is applied from the stance leg to the swing leg and an impulsive force is generated under the post-impact swing leg foot. To avoid unwanted contact with the ground during the swing phase, the robot possesses retractable feet of negligible mass.