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Decentralized Evolution of Hexapod Gaits with Independent Leg Controllers
Gary B. Parker, John Asaro, Jim O'Connor
TL;DR
Hexapod gait optimization must address high-dimensional control and inter-leg coordination, while fixed preprogrammed gaits lack adaptability. This paper independently evolves each leg's controller and reports better convergence and locomotion fitness than cooperative coevolution, including under leg ablation.
Problem
Hexapod gait optimization involves high-dimensional control spaces and coordination across legs, while fixed preprogrammed gaits lack adaptability to environmental changes and perturbations.
Source: §1 · pp. 1–2Method
Results
Decentralized evolution consistently outperforms cooperative coevolution in convergence speed and final fitness, and achieves higher fitness across leg-ablation scenarios.
Source: §5 · p. 8Takeaways & Limitations
Abstract
from arXiv · showhide
This paper presents a novel approach to hexapod locomotion by evolving each leg's gait independently through a decentralized evolutionary algorithm. Using the Webots simulator and the Mantis hexapod robot, we optimize individual leg controllers without centralized coordination, allowing emergent behaviors to drive the development of efficient, coordinated locomotion. Our decentralized method is benchmarked against cooperative coevolution, demonstrating improved efficacy in generating stable and adaptive gaits while showing interesting emergent coordination. By enabling independent evolution of leg controllers, this method reduces the complexity of gait optimization and highlights the potential of decentralized strategies for scalable and adaptive robotic systems.
1 Introduction
Hexapod gait design is challenging because control spaces are high-dimensional and coordinated locomotion is difficult to optimize, while fixed preprogrammed gaits lack adaptability. The paper proposes independently evolved leg controllers and reports better performance than cooperative coevolution in simulation.
1 Introduction
- Hexapod gait optimization is challenging because control spaces are high-dimensional and coordination across multiple legs must be precise.Centralized control and whole-gait evolutionary approaches have produced effective solutions but can face scalability and coordination-disruption issues.Source: §1 · p. 1
- Preprogrammed gaits based on fixed trajectories or phase offsets lack adaptability to environmental changes and unexpected perturbations.These approaches were effective mainly for simple tasks and controlled environments.Source: §1 · pp. 1–2
- Cooperative coevolution decomposes gait optimization into interacting subproblems but adds complexity in maintaining system coherence.Its component interactions are managed during optimization.Source: §1 · p. 2
- Each leg controller evolves independently without knowledge of the other legs, relying on emergent behavior for coordination.The genetic algorithm evaluates fitness through the robot's overall locomotion performance.Source: §1 · p. 2
- Decentralized evolution significantly outperforms cooperative coevolution in producing efficient, coordinated gaits in simulation.The comparison uses Webots and the Mantis hexapod robot.Source: §1 · p. 3
2 Simulation Environment
The study evaluates leg controllers in a Webots simulation of the Mantis hexapod. The simulated robot retains six three-degree-of-freedom legs, with modeled joint limits and position tracking used for fitness calculations.
2 Simulation Environment
- The Webots environment uses calibrated physics, standard gravity, and friction suitable for moderate grip surfaces.The setup is intended to make locomotion efficiency and stability primarily functions of the evolved gaits rather than environmental attributes.Source: §2 · p. 3
2.1 The Mantis Hexapod
- The simulated Mantis has six legs with three degrees of freedom each, for 18 modeled joints with specified movement ranges.Coxa ranges ±90 degrees, femur +60 to -75 degrees, and tibia -120 to -20 degrees; motors move at most ±5 degrees per 32-millisecond timestep.Source: Figure 1 · p. 3, §2.1 · p. 4
- A GPS at the robot's center of mass tracks position for fitness calculations, and each leg has its own independently optimized controller.The study uses the standard Webots Mantis model as the basis for simulation.Source: §2.1 · p. 4
3 Decentralized Evolutionary Framework
The framework evolves each leg's controller independently, using sinusoidal Central Pattern Generator trajectories and a genetic algorithm. The shared robot-level fitness signal supports emergent coordination among the independently optimized legs.
3 Decentralized Evolutionary Framework
- The framework combines independently evolved leg controllers, Central Pattern Generators, and a genetic algorithm without centralized coordination.Emergent behaviors from local optimization are used to achieve globally coordinated locomotion.Source: §3 · p. 4
3.1 Central Pattern Generators
- Each joint follows a sinusoidal trajectory parameterized by amplitude, phase offset, fixed shared frequency, and positional offset.The parameters are evolved independently for each leg, with coordination emerging from shared fitness evaluation.Source: §3.1 · p. 5
3.2 Genetic Algorithm for Parameter Optimization
- The genetic algorithm evolves each leg's amplitude, phase, and offset using fitness based on the robot's overall locomotion performance.The fitness is the maximum distance traveled along the X-axis from the starting position, measured using the robot's GPS.Source: §3.2 · p. 6
- Stochastic proportionate selection, uniform crossover, and single-point mutation generate new controller populations.Populations are initialized with random parameter vectors and evolve over a predefined number of generations.Source: §3.2 · p. 6
4 Testing Methodology
The testing methodology compares decentralized evolution with cooperative coevolution using matched population sizes and evaluation-cost normalization. It measures displacement and includes single-leg ablations to test performance under actuator failure.
4 Testing Methodology
- Each method uses 300 individuals per generation, with 50 individuals allocated per leg and three real-valued parameters per joint in each chromosome.Each chromosome encodes one leg's sinusoidal control parameters.Source: §4 · p. 6
- A decentralized generation evaluates 50 gaits assembled by sampling one individual from each leg's population; cooperative coevolution evaluates controllers with the best individuals from the previous generation for other legs.Cooperative coevolution therefore requires six times as many simulation runs per generation.Source: §4 · p. 6
- Fitness is the furthest displacement along the X-axis during a 20-second evaluation window, recorded using onboard GPS.The maximum Euclidean displacement from the initial position is retained as the fitness value.Source: §4 · p. 7
- The methods are compared at equivalent simulation-step budgets using effective generations to normalize evaluation cost.The decentralized and centralized baselines run for 3,000 generations, while cooperative coevolution runs for 500; one effective generation equals one pass over 300 complete gaits.Source: §4 · p. 7
- Single-leg ablation experiments disable one leg throughout training and match total evaluations across methods.The decentralized model runs for 3,000 effective generations and cooperative coevolution for 600 effective generations in these trials.Source: §4 · p. 7
5 Results
With all six legs operational, decentralized evolution outperformed cooperative coevolution in convergence speed and final fitness. It also performed better across single-leg ablations and showed smoother, less variable convergence.
5 Results
- Across 10 runs, decentralized evolution consistently beat cooperative coevolution in convergence speed and final fitness with all six legs operational.Performance metrics were averaged over 10 independent runs for each experimental condition.Source: §5 · p. 8
- Across single-leg ablations, decentralized evolution achieved higher locomotion fitness and greater adaptability than cooperative coevolution.Each ablation disabled one leg throughout training; the reported results cover all ablation scenarios.Source: §5 · p. 8
- In all experiments, decentralized evolution showed smoother convergence and lower performance variance than cooperative coevolution.The authors interpret these findings as supporting emergent coordination and resilience to disruptions in the control structure.Source: §5 · p. 8
6 Conclusion
The paper evaluates independently evolved, CPG-based leg controllers against cooperative coevolution. It reports early-stage advantages after accounting for evaluation cost and identifies physical-platform evaluation and limited local communication as future directions.
6 Conclusion
- Each leg is controlled by an independently evolved CPG-based controller.Source: §6 · p. 8
- Decentralized evolution continued to outperform cooperative coevolution in early training after accounting for evaluation cost in effective generations.The authors suggest this indicates efficiency gains beyond simple run-time equivalence.Source: §6 · p. 8
- Future work will test the framework on physical hexapods, explore hybrid models with limited local communication, and compare against fully centralized controllers.Source: §6 · p. 8
Appendix: Leg Ablation Results
The appendix presents mean- and maximum-fitness traces over time for single-leg-disabled conditions, with each figure covering 10 independent runs.
Appendix: Leg Ablation Results
- With leg 0 disabled, the appendix reports mean fitness (Fig. 4) and maximum fitness (Fig. 5) over time across 10 independent runs.Source: Figure 4 · p. 10, Figure 5 · p. 10
- With leg 1 disabled, the appendix reports mean fitness (Fig. 6) and maximum fitness (Fig. 7) over time across 10 independent runs.Source: Figure 6 · p. 11, Figure 7 · p. 11
- With leg 2 disabled, the appendix reports mean fitness (Fig. 8) and maximum fitness (Fig. 9) over time across 10 independent runs.Source: Figure 8 · p. 11, Figure 9 · p. 11
- With leg 3 disabled, the appendix reports mean fitness (Fig. 10) and maximum fitness (Fig. 11) over time across 10 independent runs.Source: Figure 10 · p. 12, Figure 11 · p. 12
- With leg 4 disabled, the appendix reports mean fitness (Fig. 12) and maximum fitness (Fig. 13) over time across 10 independent runs.Source: Figure 12 · p. 12, Figure 13 · p. 12
- With leg 5 disabled, the appendix reports mean fitness (Fig. 14) and maximum fitness (Fig. 15) over time across 10 independent runs.Source: Figure 14 · p. 13, Figure 15 · p. 13