System Design of a Quadrupedal Galloping Machine

Abstract

Abstract-Ohio State and Stanford Universities are cooperating to construct and artificial quadruped. This quadruped has a rest leg length of 0.68m and weighs 70kg. The body is made of four single-leg modules. Each module houses an articulated 3-dof leg. The articulated leg structure uses a set of mechanical springs to store energy. The stiffness of the leg, from hip to foot, is highly nonlinear. The leg initially stiffens as the leg is compressed the first 1/3 of its range, then remains roughly constant for the remainder. This stiffening allows the leg to maintain a relatively constant working length. A cable is used to flex the knee of the quadruped. As the cable is pulled, the knee bends, tensioning the energy storage springs. This cable makes about a ¼ turn over a pulley which is concentric with the hip axis, ½ turn around a pulley at the ankle and then ¾ turn back around a second hip pulley in a direction opposite the first hip pulley. This arrangement decouples cable tension and hip torque. The non-anchored end of the cable is tensioned by a capstan. This capstan uses unique geometry to decrease holding torque and to release the cable instantly. The current top speed of this leg in a 2-dimensional test is 4.15m/s. This leg has been controlled using two control systems, both implemented on an embedded controller attached to the leg. An articulated leg presents control challenges not seen when trying to control a prismatic leg. The first controller tested is a heuristic algorithm whose parameters are updated in real time by the LevenbergMarquardt learning method. This controller is similar to the controllers used by Raibert[24], with modifications to allow for leg asymmetry. The second controller tested is a direct adaptive fuzzy controller. The fuzzy controller consists of a rule base, inference mechanism, fuzzification interface, and defuzzification interface. Fuzzification starts by mapping an input (body velocity, desired change in velocity, height) into one or more membership functions.The inference mechanism then determines the applicability of each rule to the current inputs. Defuzzification combines the recommendations of each rule in an output based upon rule certainties. The adaptation mechanism modifies the rule output centers to correct velocity errors. The adaptation mechanism gains are experimentally tuned. Once tuned, the controller quickly adapts to leg changes. Both control systems were tested with and without adaptation. Both systems more accurately tracked desired velocity with adaptation. Accurate, high resolution, high speed body attitude sensing is essential for successful quadruped operation.No existing solutions meet the project requirements. An adequate sensor system is being developed in cooperation with a commercial vendor. Initial results show that accurate position tracking is possible with currently available MEMS inertial sensors.

Horse-like walking, trotting, and galloping derived from kinematic Motion Primitives (kMPs) and their application to walk/trot transitions in a compliant quadruped robot

“…To try to exploit the potential of legged locomotion a number of solutions have been developed for robots of varying size, powered by diverse energy sources. Among these, notable examples include Fujita and Kitano (1998); Berns et al (1998); Canderle and Caldwell (2000); Nichol et al (2004); Poulakakis et al (2005); Buehler et al (2005); Zhang et al (2005); Kimura et al (2007); Raibert et al (2008); Hirose et al (2009);Semini et al (2011). Quadrupedal locomotion presents good intrinsic stability features, but the coordination of the motion of four legs is non-trivial to control.…”

Development and field testing of the FootFall planning system for the ATHLETE robots

“…The requirements-conflict for the distal joint to be both light and strong is leading some manipulation and walking robots to draw inspiration from biological systems by placing actuators further up the limb and using cables to drive the distal joints (Lovchik and Diftler, 1999), (Nichol et al, 2004), (Tsusaka and Ota, 2006), (Bowling, 2007). This change moves the center of gravity of the arm closer to its base joint (waist or shoulder) and allows more powerful motors to be used for the distal joints.…”

Optical Flow Aided Motion Estimation for Legged Locomotion

“…The difficulty is an unbounded error growth resulting from the integration of biases and non-white noise. Attitude measurement relative to gravity is limited as the landing generates accelerations greater than gravity and flight phases yield no accelerometer measurements [1].…”

“…Agile terrain motion requires the adoption of dynamic gaits that are less stable than slower walking gaits. Manifest in various biological forms with a flight phase, such locomotion presents a design challenge for the mechanical, control, and sensing systems [1]. The mechanics must be able to provide thrust power and support the subsequent landing.…”