Multi-criteria Genetic Planning Extends Simulated Continuum Robot Lifetime

In simulations of two-section and four-section continuum robots, a multi-criteria genetic algorithm kept the modeled machine operational for more routes than a similarly modified A* search in an environment dominated by single-path locations. The genetic algorithm accumulated motor and mechanical damage more slowly, distributed use among components more evenly and, within the authors’ model, extended the robot’s functional lifetime. The experiment did not test the generated routes on the physical prototype, so the result concerns simulated path planning rather than demonstrated performance in hardware.

The researchers based their simulations on a self-made tendon-driven continuum robot with two flexible sections. The complete prototype contained 15 rigid disks, each 30 millimetres in diameter and 1 millimetre high, arranged along a 3-millimetre central backbone tendon. Eight 1-millimetre side tendons passed through the disks, with four assigned to each section. Two NEMA23-31-01SD stepper motors controlled each section, giving the prototype four motors in total. Each motor provided 800 steps per revolution, and AMT222A-V absolute encoders recorded their positions. A laptop calculated paths and communicated with an ATmega2560-based controller through a UART connection. The hardware informed the simulated environments, but the robot was not instructed to execute the routes generated in the experiments.

For the simulation, each flexible section was represented as a straight, thin, weightless rod rather than a continuously deforming body. Its reachable space was divided into discrete points associated with pairs of motor coordinates. The first local environment contained both single-path points, reachable by only one trajectory, and multipath points, reachable through several trajectories. It had 165 points, including 64 reachable using motor 1 alone, 64 using motor 2 alone and 37 multipath points. The second, more abstract environment contained 61 multipath points and imposed a one-to-one mapping between motor coordinates and spatial points. Combining two sections created global environments of 27,225 states in the first case and 3,721 in the second. The number of possible configurations therefore expanded rapidly with each additional section.

The team modified A* and a genetic algorithm so that they would evaluate more than the length of a route. Both planners were paired with the Analytical Hierarchy Process, a decision-making method that derives criterion weights through manual pairwise comparisons. Four measures represented the state and expected consequences of a path: Euclidean distance, error between the robot’s tip and the requested goal, accumulated motor steps, and repeated use of environment segments as a proxy for mechanical damage to the wires or tendons. A weighted fitness function combined the measures, with a smaller value indicating a more preferable path. The researchers examined 15 weighting combinations, covering cases in which accuracy, motor wear, mechanical wear or groups of criteria received greater priority.

In the genetic algorithm, each candidate route was encoded as a chromosome containing indices of environmental points. The initial population was generated by selecting connected neighboring points rather than drawing arbitrary point sequences, which was intended to reduce circular paths and dead ends. Candidate chromosomes underwent evaluation, roulette-wheel selection, single-point crossover and random mutation. The implementation was also changed to reuse previously calculated fitness values for duplicate chromosomes. To choose a practical configuration, the researchers tested population sizes from 10 to 100 and generation counts from two to 10, with each combination run 100 times for randomly selected goals. They selected a population of 50 and three generations as the best balance between fitness value and execution time.

A* needed a different modification because its usual procedure assesses neighboring points rather than complete routes. In the adapted version, A* reconstructed the sequence already explored whenever it considered a new neighbor and applied the same weighted fitness function to that full path. This allowed the two algorithms to be compared using identical criteria, although it also increased A*’s computational workload. In 100 runs with randomly selected goals in the mixed single-path and multipath environment, A* obtained better fitness values than the genetic algorithm for 13 of the 15 weighting combinations in both the two-section and four-section models. In the abstract multipath-only environment, the methods produced more ties, and the genetic algorithm achieved better values in four weighting combinations that prioritized accuracy.

Those individual fitness results did not necessarily favor A* during sustained operation. A* repeatedly selected the same route for a given start-and-goal pair, whereas the genetic algorithm generated a more diverse collection of alternatives. Concentrating movement on a small number of segments can concentrate wear on particular cables, tendons and motor movements. The genetic algorithm’s processing time was also largely independent of environmental cardinality. By contrast, A* took almost three times as long in the 165-point local environment as in the 61-point environment, reflecting its dependence on the number of available states. The authors therefore considered the genetic approach more suitable for planning in environments whose number of reachable configurations increases sharply with the number of flexible sections.

The researchers then simulated damage accumulating over consecutive routes. Each new route began at the endpoint of the preceding route, motor-step counts were added to a database and repeated use of a segment increased its recorded mechanical wear. A segment became blocked after five uses, while the motor-damage limit was set at 500 so that simulated failures would occur sooner. The robot was considered “out of order” when it reached the motor limit or when its tip became surrounded by blocked segments. These deliberately lowered thresholds accelerated the experiment. They did not represent physical maintenance thresholds, and the study involved no physical route-execution trial in which the prototype accumulated wear.

In the mixed-path environment, the genetic algorithm generated 48 routes for the two-section robot before failure, compared with 38 for A*. For the four-section version, it generated almost twice as many routes as A*. The difference was smaller in the multipath-only environment: the genetic algorithm generated 53 routes versus 52 for A* with two sections, while both generated 50 with four sections. A* sometimes recorded lower motor and mechanical damage at its final path but failed earlier because repeated segments were blocked more quickly, trapping the tip near single-path positions. As wear accumulated, A* also required longer searches to escape dead ends, increasing processing time in the environment that more closely reflected the physical prototype’s mixed pathway structure.

Overall, the experiments reveal a trade-off between selecting a strong route for one start-and-goal pair and maintaining varied operation over repeated tasks. A* often obtained the better immediate fitness value, but the genetic algorithm spread movement across routes and slowed modeled wear, particularly where many locations had only one route. The authors present the genetic method as a better option for long-term autonomous operation as the number of flexible sections and reachable states grows. Important physical effects were omitted, however, including the added weight of extra sections, the difficulty of controlling a longer body and the energy needed to move it. Whether the simulated lifetime advantage transfers to a physical tendon-driven robot remains untested because the study did not conduct end-to-end hardware validation.

Subject of Research: Multi-criteria motion planning for simulated operational resilience in tendon-driven continuum robots

Article Title: Increasing resilience of continuum robots via motion planning algorithms

Article References: Wernecke, O., Kabin, I., Dyka, Z., Sudakov, O., & Langendoerfer, P. (2026). Increasing resilience of continuum robots via motion planning algorithms. Neural Computing and Applications, 38(20), 829. https://doi.org/10.1007/s00521-026-12612-z

Image Credits: AI Generated

DOI: 10.1007/s00521-026-12612-z

Keywords: continuum robots, genetic algorithms, A* search, motion planning, multi-criteria decision-making, robot resilience, motor wear, mechanical damage, tendon-driven robots, Increasing, resilience, continuum