Abstract
Dynamic stability allows running animals to maintain preferred speed during locomotion over rough terrain. It appears that rapid disturbance rejection is an emergent property of the mechanical system. In running robots, simple motor control seems to be effective in the negotiation of rough terrain when used in concert with a mechanical system that stabilises passively. Spring-like legs are a means for providing self-stabilising characteristics against external perturbations. In this paper, we show that a quadruped robot could be able to perform self-stable running behaviour in significantly broader ranges of forward speed and pitch rate with a suitable mechanical design, which is not limited to choosing legs spring stiffness only. The results presented here are derived by studying the stability of the passive dynamics of a quadruped robot running in the sagittal plane in a dimensionless context and might explain the success of simple, open loop running controllers on existing experimental quadruped robots. These can be summarised in (a) the self-stabilised behaviour of a quadruped robot for a particular gait is greatly related to the magnitude of its dimensionless body inertia, (b) the values of hip separation, normalised to rest leg length, and leg relative stiffness of a quadruped robot affect the stability of its motion and should be in inverse proportion to its dimensionless body inertia, and (c) the self-stable regime of quadruped running robots is enlarged at relatively high forward speeds. We anticipate the proposed guidelines to assist in the design of new, and modifications of existing, quadruped robots. As an example, specific design changes for the Scout II quadruped robot that might improve its performance are proposed.
Highlights
Negotiation of rough terrain is the most important reason for building legged robots, instead of wheeled and tracked ones
The major question is whether there exists a regime, where the system tolerates perturbations from the nominal conditions without requiring any closed loop control law. The existence of this regime raises an important ‘philosophical’ question: Is there a particular mechanical design that provides self-stabilising characteristics against external perturbations originated in leg–ground interactions or motor control? How much feedback is necessary for developing control laws to stabilise a system, which exhibits inherent self-stability by means of suitable mechanical design? The answers to these questions are not yet available
The stability analysis of the passive dynamics of robotic quadrupeds was studied in a dimensionless context, revealing further intrinsic properties of quadrupedal running and unveiling aspects of robotic quadrupeds that have similar configuration but different scale
Summary
Negotiation of rough terrain is the most important reason for building legged robots, instead of wheeled and tracked ones. Animals exhibit impressive performance in handling rough terrain and they can reach a much larger fraction of the earth landmass on foot than existing wheeled vehicles. Their robotic counterparts have not yet been benefited from the improved mobility and versatility that legs offer. Two decades ago, Raibert (1986) set the stage with his groundbreaking work on dynamic legged locomotion by introducing very simple controllers for stabilising running on his one-, two- and four-legged robots. The underlying fundamental principles exemplified by his robots were minimal actuation, coupled with a suitably designed mechanical system featuring springy legs, and simple control laws that excite the natural dynamics of the mechanical system
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