Design Principles for Energy-Efficient Legged Locomotion and Implementation on the MIT Cheetah Robot

This paper presents the design principles for highly efficient legged robots, the implementation of the principles in the design of the MIT Cheetah, and the analysis of the high-speed trotting experimental results. The design principles were derived by analyzing three major energy-loss mechanisms in locomotion: heat losses from the actuators, friction losses in transmission, and the interaction losses caused by the interface between the system and the environment. Four design principles that minimize these losses are discussed: employment of high torque-density motors, energy regenerative electronic system, low loss transmission, and a low leg inertia. These principles were implemented in the design of the MIT Cheetah; the major design features are large gap diameter motors, regenerative electric motor drivers, single-stage low gear transmission, dual coaxial motors with composite legs, and the differential actuated spine. The experimental results of fast trotting are presented; the 33-kg robot runs at 22 km/h (6 m/s). The total power consumption from the battery pack was 973 W and resulted in a total cost of transport of 0.5, which rivals running animals' at the same scale. 76% of the total energy consumption is attributed to heat loss from the motor, and the remaining 24% is used in mechanical work, which is dissipated as interaction loss as well as friction losses at the joint and transmission.United States. Defense Advanced Research Projects Agency (M3 Program

Control Implementation of Dynamic Locomotion on Compliant, Underactuated, Force-Controlled Legged Robots with Non-Anthropomorphic Design

The control of locomotion on legged robots traditionally involves a robot that takes a standard legged form, such as the anthropomorphic humanoid, the dog-like quadruped, or the bird-like biped. Additionally, these systems will often be actuated with position-controlled servos or series-elastic actuators that are connected through rigid links. This work investigates the control implementation of dynamic, force-controlled locomotion on a family of legged systems that significantly deviate from these classic paradigms by incorporating modern, state-of-the-art proprioceptive actuators on uniquely configured compliant legs that do not closely resemble those found in nature. The results of this work can be used to better inform how to implement controllers on legged systems without stiff, position-controlled actuators, and also provide insight on how intelligently designed mechanical features can potentially simplify the control of complex, nonlinear dynamical systems like legged robots. To this end, this work presents the approach to control for a family of non-anthropomorphic bipedal robotic systems which are developed both in simulation and with physical hardware. The first is the Non-Anthropomorphic Biped, Version 1 (NABi-1) that features position-controlled joints along with a compliant foot element on a minimally actuated leg, and is controlled using simple open-loop trajectories based on the Zero Moment Point. The second system is the second version of the non-anthropomorphic biped (NABi-2) which utilizes the proprioceptive Back-drivable Electromagnetic Actuator for Robotics (BEAR) modules for actuation and fully realizes feedback-based force controlled locomotion. These systems are used to highlight both the strengths and weaknesses of utilizing proprioceptive actuation in systems, and suggest the tradeoffs that are made when using force control for dynamic locomotion. These systems also present case studies for different approaches to system design when it comes to bipedal legged robots

Online Planning for Autonomous Running Jumps Over Obstacles in High-Speed Quadrupeds

This paper presents a new framework for the generation of high-speed running jumps to clear terrain obstacles in quadrupedal robots. Our methods enable the quadruped to autonomously jump over obstacles up to 40 cm in height within a single control framework. Specifically, we propose new control system components, layered on top of a low-level running controller, which actively modify the approach and select stance force profiles as required to clear a sensed obstacle. The approach controller enables the quadruped to end in a preferable state relative to the obstacle just before the jump. This multi-step gait planning is formulated as a multiple-horizon model predictive control problem and solved at each step through quadratic programming. Ground reaction force profiles to execute the running jump are selected through constrained nonlinear optimization on a simplified model of the robot that possesses polynomial dynamics. Exploiting the simplified structure of these dynamics, the presented method greatly accelerates the computation of otherwise costly function and constraint evaluations that are required during optimization. With these considerations, the new algorithms allow for online planning that is critical for reliable response to unexpected situations. Experimental results, for a stand-alone quadruped with on-board power and computation, show the viability of this approach, and represent important steps towards broader dynamic maneuverability in experimental machines.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) ProgramKorean Agency for Defense Development (Contract UD1400731D

Design Principles for a Family of Direct-Drive Legged Robots

This letter introduces Minitaur, a dynamically running and leaping quadruped, which represents a novel class of direct-drive (DD) legged robots. We present a methodology that achieves the well-known benefits of DD robot design (transparency, mechanical robustness/efficiency, high-actuation bandwidth, and increased specific power), affording highly energetic behaviors across our family of machines despite severe limitations in specific force. We quantify DD drivetrain benefits using a variety of metrics, compare our machines\u27 performance to previously reported legged platforms, and speculate on the potential broad-reaching value of “transparency” for legged locomotion. For more information: Kod*lab

Hierarchical controller for highly dynamic locomotion utilizing pattern modulation and impedance control : implementation on the MIT Cheetah robot

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 105-111).This thesis presents a hierarchical control algorithm for quadrupedal locomotion. We address three challenges in developing a controller for high-speed running: locomotion stability, control of ground reaction force, and coordination of four limbs. To tackle these challenges, the proposed algorithm employs three strategies. Leg impedance control provides programmable virtual compliance of each leg which achieve self-stability in locomotion. The four legs exert forces to the ground using equilibrium-point hypothesis. A gait pattern modulator imposes a desired footfall sequence. The control algorithm is verified in a dynamic simulator constructed using MATLAB and then in the subsequent experiments on the MIT Cheetah robot. The experiments on the MIT Cheetah robot demonstrates high speed trot running reaching up to the speed of 6 m/s on a treadmill. This speed corresponds to a Froude number (Fr = 7.34), which is comparatively higher than other existing quadrupedal robots.by Jongwoo Lee.S.M

Design Of Proprioceptive Legged Robots

It has been twenty years since the advent of the first power-autonomous legged robots, yet they have still not yet been deployed at scale. One fundamental challenge in legged machines is that actuators must perform work at relatively high speed in swing but also at high torque in stance. Legged machines must also be able to “feel” the reaction forcesin both normal (to switch from swing to stance control) and tangential (to detect slip or stubbing) directions for appropriate gait-level control. This “feeling” can be accomplished by explicit force/torque sensors in the foot/leg/actuator, or by measuring the deflection of a series mechanical spring. In this thesis we analyze machines that obtain this force information directly through the implementation of highly backdriveable actuators that require no additional sensors (apart from those already required for commutation). We address the holistic design of robots with backdriveable actuators including motor, transmission, compliance, degrees of freedom, and leg design. Moreover, this work takes such actuators to the conceptual limit by removing the gearbox entirely and presenting the design and construction of the first direct-drive legged robot family (a monopod, a biped, and a quadruped). The actuator analysis that made these direct-drive machines possible has gained traction in state of the art modestly geared machines (legged robots as well as robot arms), many of which now use the same motors. A novel leg design (the symmetric five-bar, where the “knee” is allowed to ride above the “hip”) decreases the wasted Joule heating by four per unit of torque produced over the workspace compared to a conventional serial design, making the 40 cm hip-to-hip Minitaur platform possible without violating the thermal limit of its motors. A means of comparing actuator transparency (the curve representing collision energy vs. contact information) is presented and is used to compare the performance of actuators with similar continuous torque but vastly different gear ratios (1:1, 4.4:1, 51:1). This transparency can be used to show the different outcomes in a representative task where the actuators must “feel” a ball on a track through contact and then recirculate to “cage” the ball before the energy required to “feel” has caused the ball to roll out of the workspace. For a 50 g rubber ball, the direct drive actuator is able to successfully accomplish the task, but the 4.4:1 actuator is not able to cage the ball in time, and the 51:1 actuator cannot feel the ball at all before pushing it out of the workspace. Finally, the actuation and force measurement/estimation strategies of the three leading commercial legged robots are compared, alongside other considerations for real-world fielded machines. This thesis seeks to show that legged robots (both academic and commercial) whose actuators are designed with careful consideration for proprioception can have similar performance to more conventional machines, with better robustness and greatly reducedcomplexity

On Passive Quadrupedal Bounding with Flexible Linear Torso

This paper studies the effect of flexible linear torso on the dynamics of passive quadruped bounding. A reduced-order passive and conservative model with linear flexible torso and springy legs is introduced. The model features extensive spine deformation during high-speed bounding, resembling those observed in a cheetah. Fixed points corresponding to cyclic bounding motions are found and calculated using numerical return map methodologies. Results show that the corresponding robot gaits and the associated performance resemble those of its natural counterparts