Parallel stiffness in a bounding quadruped with flexible spine

Abstract

Legged locomotion involves periodic negative and positive work, which usually results in high power consumption. Improvement of the energy efficency is possible by using energy storage elements to reversibly store the negative work performed during a walking or running cycle. While series elastics with high impedance (high gear ratio) actuators are widely used, we investigate the application of parallel stiffness with highly backdriveable actuators. We specifically show that the use of parallel springs in a bounding quadruped with a flexible spine can lower power consumption by over 50%. I. INTRODUCTIONIn legged locomotion, every gait cycle involves both positive and negative work. Because most actuators cannot store negative work, the application of series compliance in walking robots is a widely used approach to increase energyefficiency (see for instance [1]-[4]). When high running speed is desired, the series compliance is often forgone to obtain a higher force bandwidth or control authority ([5]-[7]), sacrificing the energetic advantage of reversible, passive storage.Although with the series compliance approach low mechanical cost-of-tranport can be achieved, it should be noted that even when an electric actuator does not deliver any mechanical power, most will still use electrical power due to (thermal) losses, e.g. through coil resistance. Nonbackdriveable (high gear ratio) motors with series compliance can reduce loss during negative work, but the effective inertia becomes very large and the force bandwidth goes down.Very little attention has gone to the application of parallel stiffness, even though it enables the use of springs for reversible energy storage-even on existing systems-without complicating control or changing the actuator bandwidth. Duindam and Stramigioli [8] have conceptually shown that parallel springs with backdriveable actuators can lead to energy-efficient locomotion; and Yang et al. [9] have proven its merit in a bipedal robot.In this paper we investigate the application of parallel stiffness to a high-speed running quadruped, the MITCheetah, employing the passive energy storage to reduce power consumption. In Section II we introduce the system: both the robot and the dynamic model used for simulations. Section III describes the simulation experiment; the application of parallel springs is discussed in Section IV. Then we show the effect of applying optimal parallel springs in Section V and finally we discuss these results and possible future research on this subject in Section VI.

Empirical validation of a spined sagittal-plane quadrupedal model

“…Following [11], [12], [13], [15], [18], we propose a reduced-order sagittal-plane spined quadrupedal model consisting of two bipedal body segments connected by a massless pin joint 3 as shown in Figure 1. We take the state of the model to be given by q = (x, z, φ, ψ)…”

“…Progress towards this goal was made by the servo-driven Bobcat robot utilizing off-board power [14]. The design of the power-autonomous MIT Cheetah utilizing core actuation is presented in [15] but only simulation data Electrical and Systems Engineering Department, University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104 {jdup,kod}@seas.upenn.edu appears to be given. Other spined platforms exist such as the Canid robot but have only been documented executing non-steady-state tasks [16], [17], [18].…”

Core Actuation Promotes Self-manipulability on a Direct-Drive Quadrupedal Robot

“…Simplified models of quadrupedal platforms, such as the one depicted in Figure 1(a), often take the form of three-degree-of-freedom rigid bodies with common distances between the hips and mass center [16,17] and assume massless legs able to apply wrenches on the mass center when in contact with the ground subject to friction cone constraints. Following [6,7,8,9], we add core actuation to this model by introducing an actuated revolute joint to the body, depicted in Figure 1(b) (note that alternative formulations exist, such as [5]). Here we make the simplifying assumption that the parameters of each body segment are equal and that the mass center of each body segment is aligned with the leg hip, as is approximately true for the machine presented in Section 3.…”

“…Experimental work involving core actuation has been more limited. The design of power-autonomous quadrupeds utilizing parallel stiffness is presented in [9] and [10]. Other experiments have suggested increased running speed [11] and gait transition stability [12].…”

Piecewise linear spine for speed–energy efficiency trade-off in quadruped robots

“…In [11][12][13], tendon-driven robots with flexible spine has been preliminary studied. Excluding some recently unveiled robots such as MIT cheetah [14] and Boston Dynamics cheetah [15], most of the existing semi-passive quadruped robots have rigid spines and do not move very fast. It is, however, shown that fast animals, such as cheetahs and tigers, benefit from flexible spines while running [16].…”