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Abstract Until recently, most four-legged robots have lacked a feature that is found again and again in nature—a tail. Studies of animal locomotion and robots in the laboratory indicate that leaving out tails has been a design drawback. In fact, research conducted by our lab at Virginia Tech has shown that an articulated robotic tail can effectively maneuver and stabilize a quadruped both for static and dynamic locomotion. 

This paper presents the design, modeling, analysis, and experimental results of a novel bipedal robotic system that utilizes two interconnected single degree-of-freedom (DOF) leg mechanisms to produce stable forward locomotion and steering. The single DOF leg is actuated via a Reuleaux triangle cam-follower mechanism to produce a constant body height foot trajectory. Kinematic analysis and dimension selection of the Reuleaux triangle mechanism is conducted first to generate the desired step height and step length. Leg sequencing is then designed to allow the robot to maintain a constant body height and forward walking velocity. Dynamic simulations and experiments are conducted to evaluate the walking and steering performance. The results show that the robot is able to control its body orientation, maintain a constant body height, and achieve quasi-static locomotion stability. 

The traditional locomotion paradigm of quadruped robots is to use dexterous (multi degrees of freedom) legs and dynamically optimized footholds to balance the body and achieve stable locomotion. With the introduction of a robotic tail, a new locomotion paradigm becomes possible as the balancing is achieved by the tail and the legs are only responsible for propulsion. Since the burden on the leg is reduced, leg complexity can be also reduced. This paper explores this new paradigm by tackling the dynamic locomotion control problem of a reduced complexity quadruped (RCQ) with a pendulum tail. For this specific control task, a new control strategy is proposed in a manner that the legs are planned to execute the open-loop gait motion in advance, while the tail is controlled in a closed-loop to prepare the quadruped body in the desired orientation. With these two parts working cooperatively, the quadruped achieves dynamic locomotion. Partial feedback linearization (PFL) controller is used for the closed-loop tail control. Pronking, bounding, and maneuvering are tested to evaluate the controller’s performance. The results validate the proposed controller and demonstrate the feasibility and potential of the new locomotion paradigm. 

Abstract An extensible continuum manipulator (ECM) has specific advantages over its nonextensible counterparts. For instance, in certain applications, such as minimally invasive surgery or pipe inspection, the base motion might be limited or disallowed. The additional extensibility provides the robot with more dexterous manipulation and a larger workspace. Existing continuum robot designs achieve extensibility mainly through artificial muscle/pneumatic, extensible backbone, concentric tube, and base extension, etc. This article proposes a new way to achieve this additional motion degree-of-freedom by taking advantage of the rigid coupling hybrid mechanism concept and a flexible parallel mechanism. More specifically, a rack and pinion set is used to transmit the motion of the i-th subsegment to drive the (i+1)-th subsegment. A six-chain flexible parallel mechanism is used to generate the desired spatial bending and one extension mobility for each subsegment. This way, the new manipulator can achieve tail-like spatial bending and worm-like extension at the same time. Simplified kinematic analyses are conducted to estimate the workspace and the motion nonuniformity. A proof-of-concept prototype was integrated to verify the mechanism’s mobility and to evaluate the kinematic model accuracy. The results show that the proposed mechanism achieved the desired mobilities with a maximum extension ratio of 32.2% and a maximum bending angle of 80 deg. 

Synopsis Serpentine tail structures are widely observed in the animal kingdom and are thought to help animals to handle various motion tasks. Developing serpentine robotic tails and using them on legged robots has been an attractive idea for robotics. This article presents the theoretical analysis for such a robotic system that consists of a reduced complexity quadruped and a serpentine robotic tail. Dynamic model and motion controller are formulated first. Simulations are then conducted to analyze the tail’s performance on the airborne righting and maneuvering tasks of the quadruped. Using the established simulation environment, systematic analyses on critical design parameters, namely, the tail mounting point, tail length, torso center of mass (COM) location, tail–torso mass ratio, and the power consumption distribution, are performed. The results show that the tail length and the mass ratio influence the maneuvering angle the most while the COM location affects the landing stability the most. Based on these design guidelines, for the current robot design, the optimal tail parameters are determined as a length of two times as long as the torso length and a weight of 0.09 times as heavy as the torso weight. 

An extensible continuum manipulator (ECM) has specific advantages over its non-extensible counterparts. For instance, in certain applications, such as minimally invasive surgery or tube inspection, the base motion might be limited or disallowed. The additional extensibility provides the robot with more dexterous manipulation and larger workspace. Existing continuum robot designs achieve extensibility mainly through artificial muscle/pneumatic, extensible backbone, concentric tube, and base extension etc. This paper proposes a new way to achieve this additional motion degree of freedom by taking advantage of the rigid coupling hybrid mechanism concept and a flexible parallel mechanism. More specifically, a rack and pinion set is used to transmit the motion of the i-th subsegment to drive the (i+1)-th subsegment. A six-chain flexible parallel mechanism is used to generate the desired spatial bending and one extension mobility for each subsegment. This way, the new manipulator is able to achieve tail-like spatial bending and worm-like extension at the same time. A proof-of-concept prototype was integrated to verify the mobility of the new mechanism. Corresponding kinematic analyses are conducted to estimate the workspace and the motion non-uniformity.

 

Abstract This paper presents the design, dynamic modeling, and integration of a single degree of freedom (DOF) robotic leg mechanism intended for tailed quadruped locomotion. The design employs a lightweight six-bar linkage that couples the hip and knee flexion/extension joints mechanically, requiring only a single degree of actuation. By utilizing a parametric optimization, a unique topological arrangement is achieved that results in a foot trajectory that is well suited for dynamic gaits including trot-running, bounding, and galloping. Furthermore, a singular perturbation is introduced to the hybrid dynamic framework to address the lack of robust methods that provide a solution for the differential algebraic equations (DAEs) that characterize closed kinematic chain (CKC) structures as well as the hybrid nature of legged locomotion. By approximating the system dynamics as ordinary differential equations (ODEs) and asymptotically driving the constraint error to zero, CKCs can adopt existing real-time model-based/model-predictive/hybrid-control frameworks. The dynamic model is verified through simulations and the foot trajectory was experimentally validated. Preliminary open-loop planar running demonstrated speeds up to 3.2 m/s. These advantages, accompanied by low-integration costs, warrant this leg as a robust, effective platform for future tailed quadruped research. 

Abstract Based on observations from nature, tails are believed to help animals achieve highly agile motions. Traditional single-link robotic tails serve as a good simplification for both modeling and implementation purposes. However, this approach cannot explain the complicated tail behaviors exhibited in nature where multi-link structures are more commonly observed. Unlike its single-link counterpart, articulated multi-link tails essentially belong to the serial manipulator family which possesses special motion transmission design challenges. To address this challenge, a cable-driven hyper-redundant design becomes the most used approach. Limited by cable strength and elastic components, this approach suffers from low-frequency response, inadequate generated inertial loading, and fragile hardware, which are all critical drawbacks for robotic tails design. To solve these structure-related shortcomings, a multi-link robotic tail made up of rigid links is proposed in this paper. The new structure takes advantage of the traditional hybrid mechanism architecture, but utilizes rigid mechanisms to couple the motions between the ith link and the (i + 1)th link rather than using cable actuation. By doing so, the overall tail becomes a rigid mechanism that achieves quasi-uniform spatial bending for each segment and allows performing highly dynamic motions. The mechanism and detailed design of this new robotic tail are presented. The kinematic model was developed and an optimization process was conducted to reduce the bending non-uniformity for the rigid tail. Based on this special optimization design, the dynamic model of the new mechanism is significantly simplified. A small-scale three-segment prototype was integrated to verify the proposed mechanism's unique mobility.