From Bipedal Walking to Quadrupedal Locomotion: Full-Body Dynamics Decomposition for Rapid Gait Generation

This paper systematically decomposes a quadrupedal robot into bipeds to rapidly generate walking gaits and then recomposes these gaits to obtain quadrupedal locomotion. We begin by decomposing the full-order, nonlinear and hybrid dynamics of a three-dimensional quadrupedal robot, including its continuous and discrete dynamics, into two bipedal systems that are subject to external forces. Using the hybrid zero dynamics (HZD) framework, gaits for these bipedal robots can be rapidly generated (on the order of seconds) along with corresponding controllers. The decomposition is achieved in such a way that the bipedal walking gaits and controllers can be composed to yield dynamic walking gaits for the original quadrupedal robot — the result is the rapid generation of dynamic quadruped gaits utilizing the full-order dynamics. This methodology is demonstrated through the rapid generation (3.96 seconds on average) of four stepping-in-place gaits and one diagonally symmetric ambling gait at 0.35 m/s on a quadrupedal robot — the Vision 60, with 36 state variables and 12 control inputs — both in simulation and through outdoor experiments. This suggested a new approach for fast quadrupedal trajectory planning using full-body dynamics, without the need for empirical model simplification, wherein methods from dynamic bipedal walking can be directly applied to quadrupeds

From Bipedal Walking to Quadrupedal Locomotion: Full-Body Dynamics Decomposition for Rapid Gait Generation

This paper systematically decomposes a quadrupedal robot into bipeds to rapidly generate walking gaits and then recomposes these gaits to obtain quadrupedal locomotion. We begin by decomposing the full-order, nonlinear and hybrid dynamics of a three-dimensional quadrupedal robot, including its continuous and discrete dynamics, into two bipedal systems that are subject to external forces. Using the hybrid zero dynamics (HZD) framework, gaits for these bipedal robots can be rapidly generated (on the order of seconds) along with corresponding controllers. The decomposition is achieved in such a way that the bipedal walking gaits and controllers can be composed to yield dynamic walking gaits for the original quadrupedal robot — the result is the rapid generation of dynamic quadruped gaits utilizing the full-order dynamics. This methodology is demonstrated through the rapid generation (3.96 seconds on average) of four stepping-in-place gaits and one diagonally symmetric ambling gait at 0.35 m/s on a quadrupedal robot — the Vision 60, with 36 state variables and 12 control inputs — both in simulation and through outdoor experiments. This suggested a new approach for fast quadrupedal trajectory planning using full-body dynamics, without the need for empirical model simplification, wherein methods from dynamic bipedal walking can be directly applied to quadrupeds

Learning dynamic motor skills for terrestrial locomotion

The use of Deep Reinforcement Learning (DRL) has received significantly increased attention from researchers within the robotics field following the success of AlphaGo, which demonstrated the superhuman capabilities of deep reinforcement algorithms in terms of solving complex tasks by beating professional GO players. Since then, an increasing number of researchers have investigated the potential of using DRL to solve complex high-dimensional robotic tasks, such as legged locomotion, arm manipulation, and grasping, which are difficult tasks to solve using conventional optimization approaches. Understanding and recreating various modes of terrestrial locomotion has been of long-standing interest to roboticists. A large variety of applications, such as rescue missions, disaster responses and science expeditions, strongly demand mobility and versatility in legged locomotion to enable task completion. In order to create useful physical robots, it is necessary to design controllers to synthesize the complex locomotion behaviours observed in humans and other animals. In the past, legged locomotion was mainly achieved via analytical engineering approaches. However, conventional analytical approaches have their limitations, as they require relatively large amounts of human effort and knowledge. Machine learning approaches, such as DRL, require less human effort compared to analytical approaches. The project conducted for this thesis explores the feasibility of using DRL to acquire control policies comparable to, or better than, those acquired through analytical approaches while requiring less human effort. In this doctoral thesis, we developed a Multi-Expert Learning Architecture (MELA) that uses DRL to learn multi-skill control policies capable of synthesizing a diverse set of dynamic locomotion behaviours for legged robots. We first proposed a novel DRL framework for the locomotion of humanoid robots. The proposed learning framework is capable of acquiring robust and dynamic motor skills for humanoids, including balancing, walking, standing-up fall recovery. We subsequently improved upon the learning framework and design a novel multi-expert learning architecture that is capable of fusing multiple motor skills together in a seamless fashion and ultimately deploy this framework on a real quadrupedal robot. The successful deployment of learned control policies on a real quadrupedal robot demonstrates the feasibility of using an Artificial Intelligence (AI) based approach for real robot motion control

System Design of a Cheetah Robot Toward Ultra-high Speed

High-speed legged locomotion pushes the limits of the most challenging problems of design and development of the mechanism, also the control and the perception method. The cheetah is an existence proof of concept of what we imitate for high-speed running, and provides us lots of inspiration on design. In this paper, a new model of a cheetah-like robot is developed using anatomical analysis and design. Inspired by a biological neural mechanism, we propose a novel control method for controlling the muscles' flexion and extension, and simulations demonstrate good biological properties and leg's trajectory. Next, a cheetah robot prototype is designed and assembled with pneumatic muscles, a musculoskeletal structure, an antagonistic muscle arrangement and a J-type cushioning foot. Finally, experiments of the robot legs swing and kick ground tests demonstrate its natural manner and validate the design of the robot. In the future, we will test the bounding behaviour of a real legged system

Bio-Inspired Robotics

Modern robotic technologies have enabled robots to operate in a variety of unstructured and dynamically-changing environments, in addition to traditional structured environments. Robots have, thus, become an important element in our everyday lives. One key approach to develop such intelligent and autonomous robots is to draw inspiration from biological systems. Biological structure, mechanisms, and underlying principles have the potential to provide new ideas to support the improvement of conventional robotic designs and control. Such biological principles usually originate from animal or even plant models, for robots, which can sense, think, walk, swim, crawl, jump or even fly. Thus, it is believed that these bio-inspired methods are becoming increasingly important in the face of complex applications. Bio-inspired robotics is leading to the study of innovative structures and computing with sensory–motor coordination and learning to achieve intelligence, flexibility, stability, and adaptation for emergent robotic applications, such as manipulation, learning, and control. This Special Issue invites original papers of innovative ideas and concepts, new discoveries and improvements, and novel applications and business models relevant to the selected topics of ``Bio-Inspired Robotics''. Bio-Inspired Robotics is a broad topic and an ongoing expanding field. This Special Issue collates 30 papers that address some of the important challenges and opportunities in this broad and expanding field

Vertical hopper compositions for preflexive and feedback-stabilized quadrupedal bounding, pacing, pronking, and trotting

This paper applies an extension of classical averaging methods to hybrid dynamical systems, thereby achieving formally specified, physically effective and robust instances of all virtual bipedal gaits on a quadrupedal robot. Gait specification takes the form of a three parameter family of coupling rules mathematically shown to stabilize limit cycles in a low degree of freedom template: an abstracted pair of vertical hoppers whose relative phase locking encodes the desired physical leg patterns. These coupling rules produce the desired gaits when appropriately applied to the physical robot. The formal analysis reveals a distinct set of morphological regimes determined by the distribution of the body’s inertia within which particular phase relationships are naturally locked with no need for feedback stabilization (or, if undesired, must be countermanded by the appropriate feedback), and these regimes are shown empirically to analogously govern the physical machine as well. In addition to the mathematical stability analysis and data from physical experiments we summarize a number of extensive numerical studies that explore the relationship between the simple template and its more complicated anchoring body models. For more information: Kod*la

Investigation of an Articulated Spine in a Quadruped Robotic System.

This research quantitatively analyzes a multi-body dynamics quadrupedal model with an articulated spine to evaluate the effects of speed and stride frequency on the energy requirements of the system. The articulated model consists of six planar, rigid bodies with a single joint in the middle of the torso. All joints are frictionless and mass is equally distributed in the limbs and torso. A model with the mid-torso joint removed, denoted as the rigid model, is used as a baseline comparison. Impulsive forces and torques are used to instantaneously reset the velocities at the phase transitions, allowing for ballistic trajectories during flight phases. Active torques at the haunch and shoulder joints are used during the stance phases to increase the model robustness. Simulations were conducted over effective high-speed gaits from 6.0 - 9.0 m/s. Stride frequencies were varied for both models. An evolutionary algorithm was employed to find plausible gaits based on biologically realistic constraints and bounds. The objective function for the optimization was cost of transport. Results show a decreasing cost of transport as speed increases for the articulated model with an optimal stride frequency of 3 s$^{-1}$ and an increasing cost of transport with increasing speed for the rigid model at an optimal stride frequency of 1.4 s$^{-1}$, with a crossover in the cost of transport between the two models occurring at 7.0 m/s. The rigid model favors low speeds and stride frequencies at the cost of a large impulsive vertical force, driving the system through a long, gathered flight phase used to cover the long distances at the low stride frequencies. The articulated model prefers higher speeds and stride frequencies at the cost of a large impulsive torque in the back joint, akin to the contraction of abdomen muscles, preventing the collapse of the back. Thus, it is demonstrated that the inclusion of back articulation enables a more energetically efficient high-speed gait than a rigid back system, as seen in biological systems. Detailed analysis is provided to identify the mechanics associated with the optimal gaits of both the rigid and the articulated systems to support this claim.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89831/1/bhaueise_1.pd

From Bipedal to Quadrupedal Locomotion, Experimental Realization of Lyapunov Approaches

Possibly one of the most significant innovations of the past decade is the hybrid zero dynamics (HZD) framework, which formally and rigorously designs a control algorithm for robotic walking. In this methodology, Lyapunov stability, which is often used to certificate a dynamical system's stability, was introduced to the control law design for a hybrid control system. However, the prerequisites of precise modeling to apply the HZD methodology can often be too restrictive to design controllers for uncertain and complex real-world hardware experiments. This thesis addresses the problem raised by noisy measurements and the intricate hybrid structure of locomotion dynamics. First, the HZD methodology's construction is based on the full-order, hybrid dynamics of legged locomotion, which can be intractable for control synthesis for high-dimensional systems. This thesis studies the general structure of hybrid control systems for walking systems, ranging from 1D hopping, 2D walking, 2D running, and 3D quadrupedal locomotion on rough terrains. Further, we characterize a walking behavior--gait--as a solution (execution) to a hybrid control system. To find these solutions, which represent a "gait," we employed advanced numerical methods such as collocation methods to parse the solution-finding problem into the open- and closed-loop trajectory optimization problems. The result is that we can find versatile gaits for ten different robotic platforms efficiently. This includes bipedal running, bipedal walking on slippery surfaces, and quadrupedal robots walking on sloped terrains. The numerous solution-finding examples expand the applicability of the HZD framework towards more complex dynamical systems. Further, for the uncertain and noisy real-world implementation, the exponential stability of the continuous dynamics is an ideal but restrictive condition for hybrid stability. This condition is especially challenging to satisfy for highly dynamical behaviors such as bipedal running, which loses ground support for a short period. This thesis observes the destabilizing effect of the noisy measurements of the phasing variable. By reformulating the traditional input-to-state stability (ISS) concept into phase-uncertainty to state stability, we are able to synthesize a robust controller for bipedal running on DURUS-2D. This time+state-based controller formally guarantees stability under noisy measurements and stabilizes the 1.75 m/s running experiments. Lastly, robotic dynamics have long been characterized as the interconnection of rigid-body dynamics. We take this perspective one step further and incorporate controller design into the formulation of coupled control systems (CCS). We first view a quadrupedal robot as two bipedal robots connected via some holonomic constraints. In a dimensional reduction manner, we develop a novel optimization framework, and the computational performance is reduced to a few seconds for gait generation. Furthermore, we can design local controllers for each bipedal subsystem and still guarantee the overall system's stability. This is done by combining the HZD framework and the ISS properties to contain the disturbance induced by the other subsystems' inputs. Utilizing the proposed CCS methods, we will experimentally realize quadrupedal walking on various outdoor rough terrains.</p

Proximal Actuation of an Elastically Loaded Scissors Mechanism for the Leg Design of a Quadruped Robot

Spring Loaded Pantographs (SLPs) are frequently used in designing lightweight limbs for multi-legged robots. Quadruped robots that incorporate cable-pulled SLP legs have proven to be agile, robust and capable of conserving energy during their gait cycle. In such designs, the extension of the distal segments via the knee joint is dependent upon the length of the cable. In this article we propose the use of an Elastically Loaded Scissors Mechanism (ELS Mechanism or ELSM), which is a variant of the SLP. Driven by ’pulling’ onto the proximal joint of the scissors as opposed to the distal joint, this proposed leg utilizes the increased mechanical advantage of the scissors mechanism to ’amplify’ input angles to larger output displacement by the knee joint. Analysis and Simulations reveal that the proposed mechanism achieves increased motion speed as compared to the SLP mechanism. This, however, comes at the cost of higher load on the actuator which serves as an engineering trade-off. This is validated by experimentation using motion capture and load motor techniques of the SLP and ELS configurations in a physical quadruped robot