As we build our legged robots smaller and cheaper, stable and agile control without expensive inertial sensors becomes increasingly important. We seek to enable versatile dynamic behaviors on robots with limited modes of state feedback, specifically proprioceptive-only sensing. This work uses model-based trajectory optimization methods to design open-loop stable motion primitives. We specifically design running gaits for a single-legged planar robot, and can generate motion primitives in under 3 seconds, approaching online-capable speeds. A direct-collocation-formulated optimization generated axial force profiles for the direct-drive robot to achieve desired running speed and apex height. When implemented in hardware, these trajectories produced open-loop stable running. Further, the measured running achieved the desired speed within 10% of the speed specified for the optimization in spite of having no control loop actively measuring or controlling running speed. Additionally, we examine the shape of the optimized force profile and observe features that may be applicable to open-loop stable running in general.

Although they take many forms, legged robots rely upon springs to achieve high speed, dynamic locomotion. In this paper we examine the effect of adding parallel springs to robots that rely on virtual compliance. Specifically, we consider the trade-off between energetic efficiency and leg versatility that comes while using Parallel Elastic Actuators (PEAs). To do this, we vary the ratio of physical to virtual compliance for legged systems using a) a modified SLIP model, b) a single legged hopping robot, and c) a multibody simulation of the quadruped robot LLAMA. In each case we show that having a small physical compliance significantly improves the efficiency while also maintaining the robot's versatility.

This paper describes the design, control and initial experimental results of the quadruped robot LLAMA. Designed to operate in a human-scale world, this 67kg-class, all-electric robot is capable of rapid motion over a variety of terrains. Thanks to a unique leg configuration and custom high-torque, low gear-ratio motors, it can move omnidirectionally at speeds over 1 m/s. A hierarchical reactive control scheme allows for robust and efficient motion even under variable payloads. This paper describes the structure of the controller and outlines simulation results that probe the performance envelope of the robot suggesting payload capacities up to one third of its body weight. Initial testing shows robust motion over loose debris and a variety of ground slopes. Videos of the robot may be seen at https://tinyurl.com/llama-robot.

Energy-efficient navigation is an important technology for mobile robots because of its potential to increase the operation time of the robot. In particular, when coupled with a dynamic legged quadruped, the need for energy savings is made more apparent as payloads are limited. Due to the complexity in modeling motion and power models of these robots, a new approach is necessary to effectively motion plan for these complex robots. We accomplish this by using Sampling-Based Model Predictive optimization (SBMPO) which was extended for use on the LLAMA quadrupedal platform in simulation. SBMPO allows for direct generation of trajectories while using a heuristic-based search to speed up computations. This approach is shown to effectively motion plan while optimizing for energy consumption and maintaining the natural dynamics of the robot in a simulated environment.

Many running animals, unlike their robotic counterparts, have distinct morphologies and functional roles for their front and rear legs. In this paper we present a new control approach for a 5kg autonomous dynamic quadruped that explicitly encodes separate roles for each contralateral pair of legs. This controller utilizes a functional dynamic decomposition similar to Raibert's three part control law, but focuses on fore-aft leg specialization to regulate the robot's performance. The velocity of this controller, which exceeds 5 body lengths per sec, is compared with an improved trajectory-based controller and shown to be significantly more robust to changes in environment.