Worm-like robotic systems: Generation, analysis and shift of gaits using adaptive control

Abstract

The starting point of this work is a biologically inspired model of a worm-like locomotion system (WLLS). The mechanical model comprises discrete mass points connected by viscoelastic force actuators. Ground contact is constituted by ideal spikes which act as constraint forces, preventing backward motion for each mass point equipped with them. The distances between each two consecutive mass points are changed by an adaptive controller in order to track a reference trajectory. In combination with the ground contact via spikes, this results in a (undulatory) locomotion of the system.After presenting the aforementioned model and the adaptive controller, the construction of specific reference functions, which result in certain gaits, is described. For this purpose an existing algorithm is used; it allows for defining the number and succession of the active spikes as well as the resulting velocity. In the following gait examination, simulations for worm systems with four mass points are carried out to find a selection of those gaits most suitable in terms of actuator and spikes load. Prior to implementing the automatic gait change, simulations are carried out to determine the criteria for shifting: actuator and spike forces. With those criteria, the choice of the optimal gait depends on both locomotion speed and ground inclination. An approximation of the forces mentioned before enables a formulation of inclination-dependent speed intervals. This leads to a combination of speed adjustment and gait change that enables optimal crawling for predefined limits of actuator or spike forces.

Efficient worm-like locomotion: slip and control of soft-bodied peristaltic robots

“…Detailed custom modeling has aided design and control of segmented snake robots (Transeth et al 2009), but is not as advanced for earthworm-like robots. The changing shapes of earthworm-like segments has been modeled for inflatable segments (Steigenberger 2003, Steigenberger andAbeszer 2008), but neglected in whole-body models that focus instead on friction anisotropy (Schwebke andBehn 2013, Alexander 2003). Our model does not assume that the weight or drag is distributed uniformly on all segments, as has been assumed for some other animals' motions (Gmiterko et al 2011, Niebur and Erdos 1991, Boyle et al 2012, Wadden et al 1997.…”

“…Examples of robotic controllers include serpentine locomotion (Wu andMa 2010, Conradt andVarshavskaya 2003) and lampreylike locomotion (Crespi and Badertscher 2005). Adaptation of four-segment undulation gaits is studied in Schwebke and Behn (2013). In addition to modulating the frequency and amplitude parameters over time, a low frequency stepfunction-like discrete controller can be added to the output (Degallier et al 2011).…”

An earthworm-inspired friction-controlled soft robot capable of bidirectional locomotion

“…Note that this peristaltic wave propagates in the opposite direction of locomotion [40]. To model and replicate peristalsis-based locomotion for worminspired robots, researchers have explored a wide variety of methods, including finite-state machines [41]; genetic algorithms [34]; actuation phase coordination [42]; and adaptive controllers, which are employed to track prescribed reference lengths between segments [43].…”

“…In this section, employing a reduced-complexity dynamic model and linear systems theory, we develop the analytical tools necessary to study the motion and controllability properties of the robot described in section 3. From an abstract perspective, the dynamics of the proposed robot can described by a double-massspring-damper model [43,46,47] excited by active actuation forces and time-varying friction forces, as illustrated in figure 5. Accordingly, the extremal actuators are modeled as two blocks, with masses m 1 and m 2 , capable of varying their coefficients of friction with the supporting ground surface in real time in order to modulate the values (signed magnitudes) of the frictional forces, f 1 and f 2 in figure 5.…”

Planar locomotion of earthworm-like metameric robots

“…With the metameric robot body, independent actuators, and effective anchoring mechanisms, the robots are then able to achieve earthworm-like rectilinear locomotion by controlling the actuators following wave-like rules (Alexander, 2003; Boxerbaum et al, 2012). Research has also been extended from specifically assigned controlled rules to generic locomotion gaits, from the perspective of gait generation (Chen et al, 2001; Fang et al, 2015a; Ge et al, 2017), gait optimization (Fang et al, 2015b ; Ostrowski et al, 2000; Seok et al, 2010), and adaptive gait switching (Schwebke and Behn, 2013; Steigenberger and Behn, 2011). The retrograde peristalsis wave is the fundamental rule that has been applied in these gait studies.…”