Control of foot placement, forward velocity and body orientation of a one-legged hopping robot

Abstract

This paper intends to contribute to the study of dynamically balanced legged robots. A real-time applicable control algorithm for a planar one-legged robot is developed, which allows for locomotion on an irregular terrain. The simulated model consists of an articulated leg and a body, vertically placed upon the leg. During the stance phase the leg is supported by a massless foot. The algorithm is based on the choice of a number of objective locomotion parameters which can be changed from one hop to another. From a chosen initial configuration the robot is able to transfer to a chosen end configuration, while simultaneously controlling its forward velocity, its step length and its stepping height. The foot is thus being placed exactly on a chosen foothold. To reach this goal, the actuators track polynomial functions. The calculation of these functions is based on the objective parameters, and takes into account the constraints acting on the robot. These constraints result from the fact that during flight the center of gravity of the robot tracks a parabolic trajectory, and that the angular momentum with respect to the center of gravity is conserved. Writing the angular momentum constraint in a Caplygin form is the key to the algorithm. Promising simulation results for the algorithm are shown for two different experiments.

Optimal control of a half-circular compliant legged monopod

“…Iida and Tedrake optimized the motor control parameters of the underactuated two segment leg monopod to locomote in uneven terrain [41]. Vermuelen et al constructed polynomial functions for the flight and stance phases and optimized the locomotion parameters to perform hopping motion in complex environment [42]. Also, a stair hopping trajectory of the monopod with a flat foot was obtained by minimizing actuation energy in hopping cycle [43].…”

The Pneumatic Biped ?Lucy? Actuated with Pleated Pneumatic Artificial Muscles

“…An important example in this field is the dynamically balanced walking biped JOHNNIE (Pfeiffer et al, 2003) which at this moment is able to walk smoothly at various moderate speeds. In our department research on this topic is done by Vermeulen (2004) and Vermeulen et al (2003) where the scope is to translate objective parameters as step length, step height and walking speed into real-time calculated trajectories for all joints by means of polynomials.…”

Gait Optimization for Quadruped Rovers

“…In the first approach, the parameters defining the joint trajectories are directly optimized. This method has been used in various works, such as, 9 where joint trajectories are defined using polynomial functions. The second approach involves designing the motion of foot or toe of the legs, and obtaining the corresponding joint trajectories through the inverse kinematics model.…”