Abstract-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 33kg robot runs at 22 km/h (6 m/s). The total power consumption from the battery pack was 973 watts and resulted in a total cost of transport of 0.5, which rivals running animals' at the same scale. The 76% of total energy consumption is attributed to heat loss from the motor, and the 24% is used in mechanical work, which is dissipated as interaction loss as well as friction losses at the joint and transmission.

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Abstract-This paper introduces a bounding gait control algorithm that allows a successful implementation of duty cycle modulation in the MIT Cheetah 2. Instead of controlling leg stiffness to emulate a 'springy leg' inspired from the SpringLoaded-Inverted-Pendulum (SLIP) model, the algorithm prescribes vertical impulse by generating scaled ground reaction forces at each step to achieve the desired stance and total stride duration. Therefore, we can control the duty cycle: the percentage of the stance phase over the entire cycle. By prescribing the required vertical impulse of the ground reaction force at each step, the algorithm can adapt to variable duty cycles attributed to variations in running speed. Following linear momentum conservation law, in order to achieve a limitcycle gait, the sum of all vertical ground reaction forces must match vertical momentum created by gravity during a cycle. In addition, we added a virtual compliance control in the vertical direction to enhance stability. The stiffness of the virtual compliance is selected based on the eigenvalue analysis of the linearized Poincaré map and the chosen stiffness is 700 N/m, which corresponds to around 12% of the stiffness used in the previous trotting experiments of the MIT Cheetah, where the ground reaction forces are purely caused by the impedance controller with equilibrium point trajectories. This indicates that the virtual compliance control does not significantly contributes to generating ground reaction forces, but to stability. The experimental results show that the algorithm successfully prescribes the duty cycle for stable bounding gaits. This new approach can shed a light on variable speed running control algorithm.

Abstract-The paper presents a new force sensor design approach that maps the local sampling of pressure inside a composite polymeric footpad to forces in three axes, designed for running robots. Conventional multi-axis force sensors made of heavy metallic materials tend to be too bulky and heavy to be fitted in the feet of legged robots, and vulnerable to inertial noise upon high acceleration. To satisfy the requirements for high speed running, which include mitigating high impact forces, protecting the sensors from ground collision and enhancing traction, these stiff sensors should be paired with additional layers of durable, soft materials; but this also degrades the integrity of the foot structure. The proposed foot sensor is manufactured as a monolithic, composite structure composed of an array of barometric pressure sensors completely embedded in a protective polyurethane rubber layer. This composite architecture allow the layers to provide compliance and traction for foot collision while the deformation and the sampled pressure distribution of the structure can be mapped into three axis force measurement. Normal and shear forces can be measured upon contact with the ground, which causes the footpad to deform and change the readings of the individual pressure sensors in the array. A onetime training process using an artificial neural network is all that is necessary to relate the normal and shear forces with the multi-axis foot sensor output. The results show that the sensor can predict normal forces in the Z-axis up to 300N with a root mean squared error of 0.66% and up to 80N in the X-and Yaxis. The experiment results demonstrates a proof-of-concept for a lightweight, low cost, yet robust footpad sensor suitable for use in legged robots undergoing ground locomotion.

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In this thesis, I will describe the fabrication and characterization of a footpad based on an original principle of volumetric displacement sensing. It is intended for use in detecting ground contact forces in a running quadrupedal robot. The footpad is manufactured as a monolithic, composite structure composed of multi-graded polymers which are reinforced by glass fiber to increase durability and traction. The volumetric displacement sensing principle utilizes a hyperelastic gel-like pad with embedded magnets that are tracked with Hall-effect sensors. Normal and shear forces can be detected as contact with the ground which causes the gel-like pad to deform into rigid wells. This is all done without the need to expose the sensor. A one-time training process using an artificial neural network was used to relate the normal and shear forces with the volumetric displacement sensor output. The sensor was shown to predict normal forces in the Z-axis up to 80N with a root mean squared error of 6.04% as well as the onset of shear in the X and Y-axis. This demonstrates a proof-of-concept for a more robust footpad sensor suitable for use in all outdoor conditions.

Abstract-This paper presents a new approach to the characterization of tactile array sensors that aims to reduce the computational time needed for convergence to obtain a useful estimator for normal and shear forces. This is achieved by breaking up the sensor characterization into two parts: a linear regression portion using multivariate least squares regression, and a nonlinear regression portion using a neural network as a multi-input, multi-output function approximator. This procedure has been termed Least Squares Artificial Neural Network (LSANN). By applying LSANN on the 2nd generation MIT Cheetah footpad, the convergence speed for the estimator of the normal and shear forces is improved by 59.2% compared to using only the neural network alone. The normalized root mean squared error between the two methods are nearly identical at 1.17% in the normal direction, and 8.30% and 10.14% in the shear directions. This approach could have broader implications in greatly reducing the amount of time needed to train a contact force estimator for a large number of tactile sensor arrays (i.e. in robotic hands and skin).

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