Robophysical Modeling of Soft Limbless Locomotors
303
2 Materials and Methods
The robot consists of nine 3D printed segments attached by eight pin joints and
16 actuators, one on each side of every joint (Fig. 2A). The robot was modular
such that segments could be added, subtracted, or replaced as needed. The
bottom of each joint was designed to interface with LEGO blocks so that the
robot-ground contact could be easily changed. For this experiment, we used
LEGO wheels to create the anisotropic force needed for effective undulatory
locomotion [8].
Each segment had a rigid midline and two curved side lobes that supported
the motors, provided an attachment point for the Kevlar thread cables, and
served to protect the cables from the surroundings. On the top of each side
lobe there was a motor adapter. A joint consisted of two segments and two
motor/pulley/thread assemblies, one on each side (Fig. 2). The joints could freely
rotate in the horizontal plane but were designed to limit off-axis motion. Thus
the robot’s shape changes were largely constrained to two dimensions, although
some vertical bending was observed, as further discussed below. Each segment
had a holder for an IR reflective marker, and an OptiTrack motion capture
system (Natural Point) tracked the position of the markers.
Inoue et al. [11] developed a biologically-inspired robot with bilateral actuation using McKibben-type actuators. The goal of the McKibben-actuated robot
was to model the muscle morphology and dynamics of the animal as closely as
possible. Our interest was to understand how the passive mechanical properties
of the bilateral activation scheme facilitates navigating obstacles. For this purpose our robot has the advantage of an easily reconfigurable 3D printed design
and the thread offers negligible resistance to compressive forces.
The target waveform for the robot’s joint angles, ζ i (Fig. 2C), was a serpenoid
curve [6], ζ i (t) = ζ max sin(ks i + 2πf t). k = 1 is the spatial frequency, f = 0.3
Hz is the undulation frequency, and ζ max = 0.87 radians is the maximum joint
angle. We chose to have one wave on the body, as this was few enough waves to
be resolved with the number of joints but was also sufficient for forward motion
without excessive slipping or over-torquing motors.
The motor-pulley-thread actuators had two states, actively shortening and
passively lengthening, in which the motors were spooling and unspooling thread,
respectively. On the active side the motor tracked the serpenoid joint angle
positions, spooling the thread to reduce the gap between the pulley and adjacent
segment’s side lobe (Fig. 2C, red “on” cable). The change between active and
passive occurred when the thread was maximally shortened, at peaks of the
sinusoidal wave
1 . When a motor changed from active to passive, it would rapidly
unspool to a set position where the joint could fully close without causing tension
on the thread (Fig. 1C, black “off” cable). While the current study was focused
on unilateral activation, this setup allowed for bilateral actuation as well and
thus could be also used to explore co-contraction.
1 The sign of the commanded joint angle velocity was used to determine state.
303
2 Materials and Methods
The robot consists of nine 3D printed segments attached by eight pin joints and
16 actuators, one on each side of every joint (Fig. 2A). The robot was modular
such that segments could be added, subtracted, or replaced as needed. The
bottom of each joint was designed to interface with LEGO blocks so that the
robot-ground contact could be easily changed. For this experiment, we used
LEGO wheels to create the anisotropic force needed for effective undulatory
locomotion [8].
Each segment had a rigid midline and two curved side lobes that supported
the motors, provided an attachment point for the Kevlar thread cables, and
served to protect the cables from the surroundings. On the top of each side
lobe there was a motor adapter. A joint consisted of two segments and two
motor/pulley/thread assemblies, one on each side (Fig. 2). The joints could freely
rotate in the horizontal plane but were designed to limit off-axis motion. Thus
the robot’s shape changes were largely constrained to two dimensions, although
some vertical bending was observed, as further discussed below. Each segment
had a holder for an IR reflective marker, and an OptiTrack motion capture
system (Natural Point) tracked the position of the markers.
Inoue et al. [11] developed a biologically-inspired robot with bilateral actuation using McKibben-type actuators. The goal of the McKibben-actuated robot
was to model the muscle morphology and dynamics of the animal as closely as
possible. Our interest was to understand how the passive mechanical properties
of the bilateral activation scheme facilitates navigating obstacles. For this purpose our robot has the advantage of an easily reconfigurable 3D printed design
and the thread offers negligible resistance to compressive forces.
The target waveform for the robot’s joint angles, ζ i (Fig. 2C), was a serpenoid
curve [6], ζ i (t) = ζ max sin(ks i + 2πf t). k = 1 is the spatial frequency, f = 0.3
Hz is the undulation frequency, and ζ max = 0.87 radians is the maximum joint
angle. We chose to have one wave on the body, as this was few enough waves to
be resolved with the number of joints but was also sufficient for forward motion
without excessive slipping or over-torquing motors.
The motor-pulley-thread actuators had two states, actively shortening and
passively lengthening, in which the motors were spooling and unspooling thread,
respectively. On the active side the motor tracked the serpenoid joint angle
positions, spooling the thread to reduce the gap between the pulley and adjacent
segment’s side lobe (Fig. 2C, red “on” cable). The change between active and
passive occurred when the thread was maximally shortened, at peaks of the
sinusoidal wave
1 . When a motor changed from active to passive, it would rapidly
unspool to a set position where the joint could fully close without causing tension
on the thread (Fig. 1C, black “off” cable). While the current study was focused
on unilateral activation, this setup allowed for bilateral actuation as well and
thus could be also used to explore co-contraction.
1 The sign of the commanded joint angle velocity was used to determine state.