Towards Automatic Discovery of Agile Gaits for Quadrupedal Robots

Developing control methods that allow legged robots to move with skill and agility remains one of the grand challenges in robotics. In order to achieve this ambitious goal, legged robots must possess a wide repertoire of motor skills. A scalable control architecture that can represent a variety of gaits in a unified manner is therefore desirable. Inspired by the motor learning principles observed in nature, we use an optimization approach to automatically discover and fine-tune parameters for agile gaits. The success of our approach is due to the controller parameterization we employ, which is compact yet flexible, therefore lending itself well to learning through repetition. We use our method to implement a flying trot, a bound and a pronking gait for StarlETH, a fully autonomous quadrupedal robot

Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

In this work we present a trajectory Optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not pre-specify contact switches, timings, points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, here we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our trajectory Optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrated our approach with the robot's control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation task with multiple dynamic contact switches, we exemplarily show how optimized trajectories and control inputs can be directly applied to hardware.Comment: Video: https://youtu.be/sILuqJBsyK

Excitation and Stabilization of Passive Dynamics in Locomotion using Hierarchical Operational Space Control

This paper describes a hierarchical operational space control (OSC) method based on least square optimization and outlines different ways to reduce the dimensionality of the optimization vector. The framework allows to emulate various behaviors by prioritized task-space motion, joint torque, and contact force optimization. Moreover, a methodology is introduced to partially excite the natural dynamics of the robot by open-loop motor regulation while the entire behavior is stabilized by hierarchical OSC. As a major contribution, the presented control strategies are tested and validated in real hardware walking, trotting, and pronking experiments using a fully torque controllable quadrupedal robot

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Towards Agility: Definition, Benchmark and Design Considerations for Small, Quadrupedal Robots

Agile quadrupedal locomotion in animals and robots is yet to be fully understood, quantified or achieved. An intuitive notion of agility exists, but neither a concise definition nor a common benchmark can be found. Further, it is unclear, what minimal level of mechatronic complexity is needed for this particular aspect of locomotion. In this thesis we address and partially answer two primary questions: (Q1) What is agile legged locomotion (agility) and how can wemeasure it? (Q2) How can wemake agile legged locomotion with a robot a reality? To answer our first question, we define agility for robot and animal alike, building a common ground for this particular component of locomotion and introduce quantitative measures to enhance robot evaluation and comparison. The definition is based on and inspired by features of agility observed in nature, sports, and suggested in robotics related publications. Using the results of this observational and literature review, we build a novel and extendable benchmark of thirteen different tasks that implement our vision of quantitatively classifying agility. All scores are calculated from simple measures, such as time, distance, angles and characteristic geometric values for robot scaling. We normalize all unit-less scores to reach comparability between different systems. An initial implementation with available robots and real agility-dogs as baseline finalize our effort of answering the first question. Bio-inspired designs introducing and benefiting from morphological aspects present in nature allowed the generation of fast, robust and energy efficient locomotion. We use engineering tools and interdisciplinary knowledge transferred from biology to build low-cost robots able to achieve a certain level of agility and as a result of this addressing our second question. This iterative process led to a series of robots from Lynx over Cheetah-Cub-S, Cheetah-Cub-AL, and Oncilla to Serval, a compliant robot with actuated spine, high range of motion in all joints. Serval presents a high level of mobility at medium speeds. With many successfully implemented skills, using a basic kinematics-duplication from dogs (copying the foot-trajectories of real animals and replaying themotion on the robot using a mathematical interpretation), we found strengths to emphasize, weaknesses to correct and made Serval ready for future attempts to achieve even more agile locomotion. We calculated Servalâs agility scores with the result of it performing better than any of its predecessors. Our small, safe and low-cost robot is able to execute up to 6 agility tasks out of 13 with the potential to reachmore after extended development. Concluding, we like to mention that Serval is able to cope with step-downs, smooth, bumpy terrain and falling orthogonally to the ground

Benchmarking Agility For Multilegged Terrestrial Robots

In this paper, we present a novel and practical approach for benchmarking agility. We focus on terrestrial, multilegged locomotion in the field of bio-inspired robotics. We define agility as the ability to perform a set of different but specific tasks executed in a fast and efficient manner. This definition is inspired by the analysis of natural role models, such as dogs and horses as well as robotic systems. An evaluation of existing benchmarks in robotics is done and taken into account in our proposed benchmark. After the general definition, the actual normalized benchmarking values are defined, and measuring methods, as well as an online database for agility score collection and distribution, are presented. To provide a baseline for agile locomotion, various videos of dog-agility competitions were analyzed and agility scores calculated wherever applicable. Finally, validation and implementation of the benchmark are done with different robots directly available to the authors. In conclusion, our benchmark will enable researchers not only to compare existing robots and find out strengths and weaknesses in different design approaches, but also give a tool to define new fitness functions for optimization, learning processes, and future robots developments, intensifying the links between biology and technology even further