Duncan W. Haldane

Animal-inspired design and aerodynamic stabilization of a hexapedal millirobot

The VelociRoACH is a 10 cm long, 30 gram hexapedal millirobot capable of running at 2.7 m/s, making it the fastest legged robot built to date, relative to scale. We present the design by dynamic similarity technique and the locomotion adaptations which have allowed for this highly dynamic performance. In addition, we demonstrate that rotational dynamics become critical for stability as the scale of a robotic system is reduced. We present a new method of experimental dynamic tuning for legged millirobots, aimed at finding stable limit cycles with minimal rotational energy. By implementing an aerodynamic rotational damper, we further reduced the rotational energy in the system, and demonstrated that stable limit cycles with lower rotational energy are more robust to disturbances. This method increased the stability of the system without detracting from forward speed.

Precise dynamic turning of a 10 cm legged robot on a low friction surface using a tail

For maximum maneuverability, terrestrial robots need to be able to turn precisely, quickly, and with a small radius. Previous efforts at turning in legged robots primarily have used leg force or velocity modulation. We developed a palm-sized legged robot, called TAYLRoACH. The tailed robot was able to make rapid, precise turns using only the actuation of a tail appendage. By rapidly rotating the tail as the robot runs forward, the robot was able to make sudden 90° turns at 360 °s-1. Unlike other robots, this is done with almost no change in its running speed. We have also modeled the dynamics of this maneuver, to examine how features, such as tail length and mass, affect the robots turning ability. This approach has produced turns with a radius of 0.4 body lengths at 3.2 body lengths per second running speed. Using gyro feedback and bang-bang control, we achieve an accuracy of ± 5° for a 60° turn.

Performance analysis and terrain classification for a legged robot over rough terrain

Minimally actuated millirobotic crawlers navigate unreliably over uneven terrain-even when designed with inherent stability-mostly because of manufacturing variabilities and a lack of good models for ground interaction. In this paper, we investigate the performance of a legged robot as it traverses three distinct rough terrains: tile, carpet, and gravel. Furthermore, we present an accurate, robust, low-lag, and efficient algorithm for terrain classification that uses vibration data from the on-board inertial measurement unit and motor control data from back-EMF sensing and magnetic encoders.

Integrated Manufacture of Exoskeletons and Sensing Structures for Folded Millirobots

Inspired by the exoskeletons of insects, we have developed a number of manufacturing methods for the fabrication of structures for attachment, protection, and sensing. This manufacturing paradigm is based on infrared laser machining of lamina and the bonding of layered structures. The structures have been integrated with an inexpensive palm-sized legged robot, the VelociRoACH [Haldane et al., 2013, “Animal-Inspired Design and Aerodynamic Stabilization of a Hexapedal Millirobot,” IEEE/RSJ International Conference on Robotics and Automation, Karlsruhe, Germany, May 6–10, pp. 3279–3286]. We also present a methodology to design and fabricate folded robotic mechanisms, and have released an open-source robot, the OpenRoACH, as an example implementation of these techniques. We present new composite materials which enable the fabrication of stronger, larger scale smart composite microstructures (SCM) robots. We demonstrate how thermoforming can be used to manufacture protective structures resistant to water and capable of withstanding terminal velocity falls. A simple way to manufacture traction enhancing claws is demonstrated. An electronics layer can be incorporated into the robot structure, enabling the integration of distributed sensing. We present fabrication methods for binary and analog force sensing arrays, as well as a carbon nanotube (CNT) based strain sensor which can be fabricated in place. The presented manufacturing methods take advantage of low-cost, high accuracy two-dimensional fabrication processes which will enable low-cost mass production of robots integrated with mechanical linkages, an exoskeleton, and body and limb sensing. [DOI: 10.1115/1.4029495]

Robotic vertical jumping agility via series-elastic power modulation

Animal agility studies inspired a leg mechanism that improves power modulation and a high-jumping and wall-jumping robot. Several arboreal mammals have the ability to rapidly and repeatedly jump vertical distances of 2 m, starting from rest. We characterize this performance by a metric we call vertical jumping agility. Through basic kinetic relations, we show that this agility metric is fundamentally constrained by available actuator power. Although rapid high jumping is an important performance characteristic, the ability to control forces during stance also appears critical for sophisticated behaviors. The animal with the highest vertical jumping agility, the galago (Galago senegalensis), is known to use a power-modulating strategy to obtain higher peak power than that of muscle alone. Few previous robots have used series-elastic power modulation (achieved by combining series-elastic actuation with variable mechanical advantage), and because of motor power limits, the best current robot has a vertical jumping agility of only 55% of a galago. Through use of a specialized leg mechanism designed to enhance power modulation, we constructed a jumping robot that achieved 78% of the vertical jumping agility of a galago. Agile robots can explore venues of locomotion that were not previously attainable. We demonstrate this with a wall jump, where the robot leaps from the floor to a wall and then springs off the wall to reach a net height that is greater than that accessible by a single jump. Our results show that series-elastic power modulation is an actuation strategy that enables a clade of vertically agile robots.

Running beyond the bio-inspired regime

The X2-VelociRoACH is a 54 gram experimental legged robot which was developed to test hypotheses about running with unnaturally high stride frequencies. It is capable of running at stride frequencies up to 45 Hz, and velocities up to 4.9 m/s, making it the fastest legged robot relative to size. The top speed of the robot was limited by structural failure. We present new methods and materials to make more robust folded robotic structures. High-frequency running experiments with the robot shows that the power required to cycle its running appendages increase cubically with the stride rate. Our findings show that although it is possible to further increase the maximum velocity of a legged robot with the simple strategy of increasing stride frequency, considerations must be made for the energetic demands of high stride rates.

Automatic identification of dynamic piecewise affine models for a running robot

This paper presents a simple, data-driven technique for identifying models for the dynamics of legged robots. Piecewise Affine (PWA) models are used to approximate the observed nonlinear system dynamics of a hexapedal millirobot. The high dimension of the state space (16) and very large number of state observations (~100,000) motivated the use of statistical clustering methods to automatically choose the submodel regions. Comparisons of models with 1 to 50 PWA regions are analyzed with respect to state derivative prediction and forward simulation accuracy. Derivative prediction accuracy was shown to reduce average in-axis absolute error by up to 52% compared to a null estimator. Simulation results show tracking of state trajectories over one stride length, and the degradation of simulation prediction is analyzed across model complexity and time horizon. We describe metrics for comparing the performance of different model complexities across one-step and simulation predictions.

Roll oscillation modulated turning in dynamic millirobots

As we seek to develop more maneuverable legged robots, we need to understand the dynamics of legged turning in an approachable fashion. In this work, we analyze the dynamic turning motion of a dynamic hexapedal millirobot. We explore a family of phase locked turning gaits where all legs of the robot move at the same speed. These gaits are highly periodic, allowing the vertical height and roll angle of the robot to be approximated by single harmonic sinusoidal functions. We demonstrate that oscillations in height and roll angle determine the robots turning behavior. The phase between these oscillations (and therefore the turning behavior) was modulated by the phase between the left and right sets of legs. A simple model using compliant leg forces was shown to match turning behavior for a range of 5Hz turning gaits. Based on the finding that roll oscillations are major determinants of turning behavior, we modified the robot to create a new high speed turning gait (forward velocity: 0.4 m/s, turn rate 206°/s).

Design Exploration and Kinematic Tuning of a Power Modulating Jumping Monopod

The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot’s series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor’s limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot’s hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot’s total height that produces a simulated maximum jump power 3.6 times greater than its motor’s limit. A 0.27m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps. [DOI: 10.1115/1.4035117]

A power modulating leg mechanism for monopedal hopping

New work in robotics targets the development of controllable agile motions such as leaping. In this work, we examine animal and robotic systems on the metric of jumping agility and find that animals can outperform the most agile robots by a factor of two. These specially adapted animals use a jumping strategy we term power modulation to generate more peak power for jumping than otherwise possible. A novel eight-bar revolute mechanism designed with a new linkage synthesis approach encodes the properties for power modulation as well as constraints which assure rotation-free jumping motion. We fabricate an 85 gram prototype and demonstrate that it can perform a range of jumps while constrained by a linear slide. The prototype can deliver 3.63 times more peak jumping power than the maximum its motor can produce. A simulation matched to the physical parameters of the prototype predicts that the robot can attain an agility exceeding that of the most agile animals if the actuator power is increased to 15W.