Morphological Evolution of Physical Robots through Model-Free Phenotype Development

Abstract

Artificial evolution of physical systems is a stochastic optimization method in which physical machines are iteratively adapted to a target function. The key for a meaningful design optimization is the capability to build variations of physical machines through the course of the evolutionary process. The optimization in turn no longer relies on complex physics models that are prone to the reality gap, a mismatch between simulated and real-world behavior. We report model-free development and evaluation of phenotypes in the artificial evolution of physical systems, in which a mother robot autonomously designs and assembles locomotion agents. The locomotion agents are automatically placed in the testing environment and their locomotion behavior is analyzed in the real world. This feedback is used for the design of the next iteration. Through experiments with a total of 500 autonomously built locomotion agents, this article shows diversification of morphology and behavior of physical robots for the improvement of functionality with limited resources.

Fig 1. Developmental process.

A “mother robot” (A) is used for the automatic assembly of candidate agents from active and passive modules. For the construction process, the robotic manipulator is equipped with a gripper and a glue supplier. Each agent is represented by the information stored in its genome (B). It contains one gene per module, and each gene contains information about the module types, construction parameters and motor control of the agent. A construction sequence encoded by one gene is shown in (C). First, the part of the robot which was encoded by the previous genes is rotated (C1 to C2). Second, the new module (here active) is picked from stock, rotated (C3), and eventually attached on top of the agent (C4).

Fig 2. Construction process.

This example illustrates the execution of the third (and last) gene of the genome shown in Table 1. (a) The initial configuration shows the state after construction of the first two genes, i.e. a passive element is fixed onto an active module (labeled as structure) and a second active element is prepared. (b-c) Rotation of the structure by -90° around the z-axis and 90° around y. (d) Rotation of the new element by -90° around y. (e-f) HMA is applied to the structure and the module is connected on top of the structure according to the position offset parameters Δx and Δy. (g) An end-rotation of the whole agent by 90° around the y-axis is performed. (h) The motor control parameters are assigned to the active elements and the agent can be evaluated.

Fig 3. Evolution for a locomotion task.

In each of the five experiments, ten generations with ten robots were built and tested. For each robot of experiment 2, an image of its top-view at the beginning of the evaluation process is shown. The number on the top-left corner of each image indicates its fitness (cm/s). The lines between generations show the relations between robots, i.e. the method for generating the new genotype (solid black: elite; thin black: crossover; thin grey: mutation). Negative fitnesses and missing images indicate failure of the building process of the respective robot. The images show that various types of robots are tested, and the fitness of the robots increases in the course of the experiment.

Fig 4. Fitness evaluation and locomotion diversity.

In all experiments, the fitness increases relative to the initial generation (A). The lines show the upper quartile of the normalized fitnesses in each generation, with the errorbars indicating best and median fitness. The increasing fitness indicates that the evolutionary process applied to the initial population of robots improves their locomotion capabilities. The top view of the trajectories of four successful robots from experiments 1a, 1c and 2 shows that different locomotion strategies are applied (B). While most successful solutions result in a stable limit cycle, also more unsteady behavior (blue) can achieve a good performance.

Fig 5. Exploration of the design space.

Each agent can be located in the design space given its number of elements and shape factor (A,B,C). The grey area shows the theoretical limit which can be reached using the cubic modules. The portion of this space that can be covered is restricted by the constraints which apply to the real-world construction process. The colored areas illustrate the parts of the design space that can be reached with different sets of active constraints. All constraints are active in (A), the stability condition is relaxed in (B) and no constraints are active in (C). This subsequently increases the reachable portion of the design space. The solid black markers indicate the distribution of the agents in experiment 1b (A) and experiment 2 (B). Their area is proportional to the number of agents in the bin. The right column (D-I) shows two example morphologies per experiment.