A New Methodology for the Design of Passive Biped Robots: Determining Conditions on the Robot’s Parameters for the Existence of Stable Walking Cycles

Currently, passive robots are designed following a trial and error process in which the existence of a stable walking cycle for a given passive robot’s model is analyzed using Poincaré maps. The standard stability analysis procedure suffers from discretization aliasing, and it is not able to deal with complex passive models. In this paper a methodology that allows finding conditions on the robot’s parameters of a given passive model in order to obtain a stable walking cycle is proposed. The proposed methodology overcomes the aliasing problem that arises when Poincaré sections are discretized. Basically, it implements a search process that allows finding stable subspaces in the parameters’ space (i.e., regions with parameters’ combinations that produce stable walking cycles), by simulating the robot dynamics for different parameters’ combinations. After initial conditions are randomly selected, the robot’s dynamics is modeled step by step, and in the Poincaré section the existence of a walking cycle is verified. The methodology includes the definition of a search algorithm for exploring the parameters’ space, a method for the partition of the space in hypercubes and their efficient management using proper data structures, and the use of so-called design value functions that quantify the feasibility of the resulting parameters. Among the main characteristics of the proposed methodology are being robot independent (it can be used with any passive robot model, regardless of its complexity), and robust (stable subspaces incorporate a stability margin value that deals with differences between the robot’s model and its physical realization). The methodology is validated in the design process of a complex semi-passive robot that includes trunk, knees, and non-punctual feet. The robot also considers the use of actuators, controllers and batteries for its actuation.