Autonomous motion designs can run or climb, but few can do both and effectively transition between surfaces. Now, quantification of small-animal acrobatic behavior may inspire new miniature robotics capable of these varied motion profiles — for sentinel and search-and-rescue disaster missions.

High-speed videography, mathematical modeling, and prototyping are helping researchers recreate lizard-righting motion and pendulum-type maneuvers in robotics. One recent study carried out by Ardian Jusufi and colleagues at the University of California, Berkeley, demonstrates how large-tailed animals avoid injury by flipping to land on their feet.

“It is not immediately obvious which mechanism an animal will use to accomplish aerial righting. Depending on body size, morphology, and mass distribution, there are multiple strategies,” says Jusufi.

The robot used to verify 3D righting-motion models consists of body and tail, plus a gyroscope that senses body position and sends feedback to a tail-positioning motor. This control effectively transfers angular momentum from body to tail.

Physics and kinematics

When presented with an inclined ledge to a gap, not all animals take a leap. Another investigation by some of the same researchers (Rapid Inversion: Running Animals and Robots Swing like a Pendulum under Ledges at details the kinematically unique ability of some creatures to swing around a ledge in a rapid scurry movement. Understanding such complex environment negotiation (and its rapid transfer and redirection of energy) offers new biomechanics insights — enabling similar motion designs allowing dynamic reconfiguration. Such abilities could also be integrated into miniature motion devices for autonomous use.

Using a pendulum-like swing with hind legs as grappling hooks, the small, legged animals use natural body and appendage dynamics to effectively complete the maneuver.

The DASH robot in the initial engineered design incorporates a single dc motor aligned so that its circular output lies in the sagittal plane. (The dc motors provide better stroke lengths, efficiencies, and power densities than other actuators such as piezoelectric actuators.) Stiff linkages and polymer hinges transfer power from the motor to the legs; circular input trajectory forces spur the end to trace a similar motion output. During turning, a shape-memory alloy TOKI SmartServo RC-1 pulls on the DASH’s front frame corners, resulting in skew and an induced turn. Feed-forward commands are communicated via Bluetooth.

Honing a pendulum model

Swing kinematics are most simply modeled as a pendulum with zero transfer of kinetic energy. However, pendulum models with some kinetic-energy transfer better match actual robot and animal trajectories, especially at the swing onset — suggesting that energy is effectively transferred from linear motion to swinging with about 20% of total energy lost in the process.

Honing the rapid-inversion model further, energy losses likely occur due to a trajectory discontinuity (during the transition from running to swinging) and its redirection of kinetic energy. Actual trajectories, though more rapid than a passive pendulum, lag near the end of the cycle — probably due to damping.

Motion controls

The prototype robotics use only passive dynamics and feedforward motion models, but future iterations could map more sophisticated controls. During the transition from running to swinging, the middle and front legs of cockroaches continue to cycle in free air, while the hind legs hook the ledge via claws: Here, cockroaches could complement task-level feedback for claw engagement with a feedforward mode. In fact, pattern generators providing signals to muscle-controlling limbs have flexible control architecture capable of decoupling the action of legs. In contrast, geckos don’t leg cycle, suggesting alternate control responses.

Practical manufacturing

Traditionally, microrobots appropriate for the motion tasks described here have been difficult to design using precision machining or microelectromechanical systems (MEMS) technology because of the challenge in constructing high-strength segments with low-loss joints on the mm and μm scale. Now, new fabrication processes such as smart composite microstructures can integrate rigid links and large-angle flexure joints through laser micromachining and lamination. In addition, rapid inversion is not a sustained activity, so energy efficiency is less important than effective energy transfer to stably complete the motion as quickly as possible.

Related link: Snake-inspired search-and-rescue robots:

Sizing motors for legged robotics

Applying Nature’s inertial-assisted approaches in commercial robotics applications (see Robotic stability taking cues from Nature) requires unique approaches to motor sizing and selection.

Choosing appropriate motors for autonomous legged robots poses challenges not typically faced by designers in other domains of mechatronics and electromechanical automation. The highly varied and fundamentally intermittent nature of a running, climbing, or crawling machine’s interactions with its environment combined with the limitations of contemporary actuator power density narrow design choices — for which constraints are hard to characterize. Currently, many designers rely heavily on empirical trial and error; many versions of a robot are built with iteratively better motor-gearbox choices.

Another method is to pick a single speed-torque operating point and specify a motor that outputs this at continuous steady-state operation. Still another approach employs dynamic simulations with empirical “generate and test” cycles iterated in software.

An improved approach to motor sizing is based on mathematically generated guidelines while enforcing constraints of the interaction of motor thermal and dynamic behavior with the application.

Selection of robot motors and gearboxes is traditionally driven by industrial applications, in which a task consists of a known target trajectory, accomplished by an appropriately sized actuator — as for a robotic arm in an assembly line that lifts and precisely maneuvers a specified part. However, in the realm of legged robots, motor capabilities (and damage and failure conditions) and robot behavior (leg trajectories) cannot be neatly segregated.

Coupling motor operation with the thermal consequences of the application optimizes actuator performance while avoiding thermal damage. In short, numerical simulations are run over the space of commercially available motors. The resulting algorithm produces notably different values from conventional motor-sizing methods (that either ignore thermal considerations entirely, or impose overly conservative current limits based on the permissible ceiling associated with continuous steady-state operation.)

Results validate passive-elastic energy storage to enable more continuous actuator power delivery, and development (through mechanical design) of an approximately constant motor speed.

Consider a 1-DOF vertical climbing robot in which the actuator must lift a constant mass vertically against gravity, absent any friction. Assume it generates motor trajectories across myriad regimes in the (fixed-voltage) speed-torque operational plane. Even for applications with strikingly different requirements, computations can determine motor characteristics affecting output motion, and development of motor-gearbox selection aids.

Simplifying the traditional library of trajectories to a single dynamic model generates a summarized family of speed-torque challenges likely to be encountered. The motor can either be running continuously (so constant voltage is applied to the motor terminals) or intermittently. The former represents a robot with wheels rolling up a pole, while intermittent operation corresponds to a legged robot that bounds or leaps upward. Within this very specific task domain, it’s demonstrated that legged robots (morphologically constrained to intermittent loading) pose a fundamentally different set of requirements for motor selection than do wheeled robots, in which continuous power delivery is acceptable.

Download the original paper in its entirety at