Journal of Membrane Computing

, Volume 1, Issue 4, pp 262–269 | Cite as

Membrane computing models and robot controller design, current results and challenges

  • Cătălin BuiuEmail author
  • Andrei George Florea
Regular Paper


Designing membrane controllers for single- and multi-robot systems is an application area initiated in 2011 at the Laboratory of Natural Computing and Robotics (natuRO) of the Politehnica University of Bucharest. In this paper, an overview of natuRO’s research on the design of robot controllers based on various models of membrane systems is given. After an introduction to robotics and natural computing, this paper follows multiple directions. Firstly, a description of three membrane system simulators is given, taking into account their evolution, comparative capabilities, and application areas for each of them. Secondly, the main part of this paper is a synopsis of the applications of membrane systems in robot control, while an emphasis is paid to the new membrane computing models introduced at natuRO, Enzymatic Numerical P Systems and XP colonies, and their specific use in single- and multiple-robot applications. Thirdly, the paper continues with a critical overview of the performances of membrane controllers as compared to traditional ways to control single- and multiple-robot systems, current challenges and possible ways to overcome these. Example avenues for future related works are given in the conclusion.


Membrane computing Numerical P systems Robotics Robot control Multi-robot systems Drones Embedded system 

1 Introduction to robotics and natural computing

Robotics deals with the design, creation, operation, and use of robots. Robots are advanced mechatronic systems that are able to act on behalf of human users to fulfill tasks that are too difficult, too dangerous, too dirty, etc. for humans to perform. Robots are endowed with multiple sensors that allow them to sense the environment, and with actuators and end-effectors that allow them to act upon (and modify) the environment. In between the sensors and actuators/end-effectors lies the “brain” of the robot, or the robot controller(s). In a way, one can say that robotics (in general) is (concerned with the design of) the “intelligent” connection between sensing and action.

Robots and robotics technology are involved in a large number of market domains [29]: manufacturing domain, healthcare, agriculture domain, civil, commercial, transport and logistics, and consumer, and consequentlty the applications are extremely diverse, e.g., machining [32], window cleaning [31], robotic surgery [31], human-robot interaction [6], etc.

Robot technologies and their respective purposes are classified in Table 1 according to [29].
Table 1

Robot technologies and their end result

Robot technology


Systems Development

Better systems and tools

Human Robot Interaction

Better interaction


Making better machines

Perception, Navigation and Cognition

Better action and awareness

General robot abilities identified in [29] include the following: adaptability, cognitive ability, configurability, decisional autonomy, dependability, interaction ability, manipulation ability, motion ability, and perception ability. Cognitive abilities include the following: action, interpretative, envisioning, learning, and reasoning abilities. Of particular interest to natuRO is the development of reasoning abilities for robots and drones (see Fig. 1 for the robots and drones in use at natuRO) while obtaining decisional autonomy.
Fig. 1

Robots and drones at naturRO

Robotics nowadays faces big challenges and reference [36] had identified the 30 most important topics and research directions in robotics through an online survey. These challenges were further refined into ten grand challenges, see Table 2.
Table 2

Top ten grand challenges in robotics


Robotics grand challenges


New materials and fabrication schemes


Biohybrid and bioinspired robots


New power sources, battery technologies, and energy-harvesting schemes


Robot swarms


Navigation and exploration in extreme environments


Fundamental aspects of artificial intelligence (AI) for robotics


Brain–computer interfaces


Social interaction


Medical robotics


Ethics and security

A particular area that naturRO is very much interested in is the fourth in the table above, swarm robotics. A robotic swarm is composed of many (so many that are difficult to count) simple (rudimentary) robots, usually with limited sensory capabilities and inter-robot communication mechanisms. Most of the time the communication between robots is indirect, i.e., through the environment (see the concept of stigmergy detailed below). Some of the experiments described in this overview involved simulated and real swarms of Kilobot robots (Figs. 2 and  3).

Some of the recent natuRO experiments have utilized robot-operating system (ROS), which is the most used open-source robotics middleware [37].

It is traditionally considered that natural computing concerns three classes of methods [7]:
  1. 1.

    bioinspired problem-solving techniques;

  2. 2.

    the use of natural materials for computations;

  3. 3.

    the use of computers to replicate natural phenomena.

Natural computing paradigms have been proven to be successful in a large number of diverse application areas, among which is the control of robots.

Among the most known natural computing paradigms are fuzzy logic, neural networks, evolutionary algorithms, swarm intelligence, DNA computing, artificial immune systems and many others.

Fuzzy logic systems have a long tradition of successful applications in designing controllers for robots and autonomous vehicles. Nowadays, this is still a fruitful area, with diverse applications, such as for soccer robots [1] and mobile robot navigation [22, 23].

Neural networks have been successfully applied to the control of robotic manipulators and mobile robots [8, 21, 35]. Evolutionary algorithms have demonstrated their power and efficiency in optimizing traditional and “intelligent” robot controllers [3, 16, 19], including a mobile robot path planning using membrane evolutionary artificial potential field [24].

Biomimetics deals with the design of artificial systems (e.g., robots) that are inspired by natural structures that evolved to optimal designs in millions of years of evolution. Biohybrid and bioinspired robots (challenge 2 in Table 2) are gaining momentum, see for example the proliferation of soft robots [17, 20].

2 Results of membrane systems applied in robot control

In 2010 the possible use of P systems (PS) in robotics was taken into consideration under the auspices of the then founded Natural Computing and Robotics Laboratory (natuRO). Academic staff and Ph. D. students affiliated with this laboratory have focused on developing robot control models using MC-based paradigms (ENPS and XPcol were introduced at natuRO):
  1. 1.

    numerical P systems (NPS);

  2. 2.

    enzymatic numerical P systems (ENPS);

  3. 3.

    P colonies (Pcol);

  4. 4.

    XP colonies (XPcol).

The first step toward usable MC-based robot controllers was the implementation of a formally correct NPS simulator called SNUPS [2]. The simulator, the first of its kind, was a Java application that created an internal model of an NPS and repeatedly executed it step by step until a specific condition was met (or the application was shut down).

The membrane systems were introduced by the user using a tree-based graphical user interface which allowed even novice users to test out models. Based on SNUPS, the first NPS-based robot controller was also introduced in [2] and evaluated in detail in [30].

However, there was room for improvement, as the controllers required a certain degree of programming knowledge from the user and were executed on top of other software stacks that also had their specific challenges.

Also, another improvement direction was in increasing the modeling power of the model by enhancing the core computational components. As such, the second step was the introduction of an NPS model extension, the ENPS [25]. This extension introduced two new computational features that proved to be necessary and useful in robotics applications. The first enabled models to simultaneously execute multiple programs, without randomly choosing one program from a set. This allowed for developing predictable robot controllers (and behaviors) that were multi-tasking. The second extension was the introduction of the (artificial) enzyme, a biological concept that in the context of MC was interpreted as a way of controlling the executability of programs using one or more special P objects. By analogy, a transistor allows the current on one electric line to control the current on a separate line, thus offering a means of dynamically changing the behavior of the circuit. In terms of MC, this means that the model can be designed to enable or disable certain programs depending on runtime conditions [25].

The study of PS-based models for robot control continued in [5], where the proposed control model was thoroughly evaluated in terms of modeling power and controller performance. The modeling power was validated by implementing various classical robot behaviors using PS, such as Braitenberg vehicles for obstacle avoidance and following the leader [5]. The controller performance was assessed by measuring the execution time of the model for each behavior.

Although current results allowed for remote robot control using MC models, the complexity of the software stack was a prohibiting factor toward deploying the control models on-board, in an embedded environment. The programming paradigms used for SNUPS (object-oriented programming in Java) were high level and required desktop PCs with multi-tasking operating systems to run. Also, the simulator and associated controllers had not been designed with resource efficiency in mind, but rather had a user-oriented design instead of an application-oriented design.

In this direction, the next step had two aims. Firstly, there was a shift toward a simpler MC model, the P colony, which was theoretically less costly to execute, and resource-wise. Secondly, due to the fact that no P colony simulator was available, one was implemented at natuRO (Lulu). This simulator was designed from the ground up with simplicity in mind and this was visible in the internal memory structure and execution loops of the simulator. These two aspects were discussed in [14], also in the context of robot control. Yet, in this case, the focus was not just on the control of a single robot, but rather a group of many, simple and (indirectly) interacting robots, known as a swarm. Thus, this paper opened the way for future research that attempted to model, not just the inputs/outputs of the robots but also their interaction as a group. The newly introduced simulator was written in Python, a modern and efficient language, and was designed to parse a text description of a Pcol model and afterward executes it step by step, all in a lightweight terminal window.

The control models introduced in [14] successfully handled a homogeneous group of swarm robots, where each robot was controlled by an individual P colony. The simulated robots in Fig. 2 individually move away from their neighbors up to a pre-specified distance. This dispersion experiment was successfully scaled up to thousands of simulated robots, as it consists of a P colony with a capacity of 3 P objects.
Fig. 2

Swarm of simulated Kilobots in a dispersion experiment

The robots were able to interact with one another using the concept of stigmergy, an information exchange mechanism that does not require direct message exchanges [18].

Although stigmergy as a mechanism is quite flexible, the robots themselves, the Kilobots [28], lacked the advanced sensory capabilities that are useful for high-level stigmergic interaction. Thus, the problem of modeling robot interactions was first tackled in [10] by using a Pcol extension, the XP colony (XPcol) which was introduced earlier in [4]. The XPcol adds a new outer membrane that encompasses other ordinary Pcol in such a way that agents from different Pcols can interact with one another using the newly introduced exteroceptive rules, an extension of the normal communication rules.
Fig. 3

Swarm of real Kilobots performing a segregation experiment

An example of a swarm of Kilobots is shown in Fig. 3, where the robots execute a color segregation experiment. Their task is to select one of the three differently colored leader from the inner circle and reach a consensus. If a consensus cannot be reached, the robots attempt to randomly move out of the communication range of their neighbors.

One of natuRO’s scientific goals is to bring MC models down from the centralized PC toward the low-level microcontroller that powers most robots, to achieve truly scalable, local control. This was finally achieved and thoroughly discussed in [11], where an embedded version of the Lulu P colony simulator and an associated robot controller were presented. The two applications were ported from Python to C and their internal models were optimized in the process. This allowed the two applications to be executed on 32 MHz microcontrollers that had only 2 KB of RAM memory and 32 KB of program memory. The implementation details as well as other technical aspects are discussed in [9].

Having obtained an embedded-ready MC robot controller, it was time for a detailed evaluation of these contributions, in direct comparison with simpler models, such as finite state machines and even with model-less applications. These results were presented in [15] in the context of distributed multi-robot applications with a key emphasis on interaction, scalability and performance. It was shown that P/XP colonies could successfully compete with simpler models and even model-less designs in applications such as distributed color segregation. This specific application was chosen for its complexity and dependency on direct information exchange between robots, an aspect that was handled at the model level using the previously introduced XPcol and exteroceptive rules. The results were validated in simulations of up to 50 robots and real swarms of 16 robots and showed that despite the higher model complexity of the proposed XPcol controller, the differences in mean execution time and energy consumption were not significant [15].

Although lightweight and efficient, Pcol and XPcol models offer only a discrete output and are thus not suitable for numerical control applications. The alternative are of course NPSs and ENPSs that were previously discussed. However, initial attempts to use these models relied on specialized code that could only be executed on a particular type of robot and was not easily portable.

Instead, one could use ROS that allows one application to interact with various types of robots by defining standard communication channels that are common across robot manufacturers and thus ensures a great level of portability [27].

To this end, a lightweight NPS and ENPS simulator called PeP was developed [12]. This simulator, coupled with an ROS-compatible robot controller, has allowed a single NPS or ENPS controller to control either a mobile robot or a drone without any source code or modifications.
Fig. 4

Drone navigation using fiducial tags and an ENPS controller

Most recently, this ROS integration of an NPS/ENPS controller was used to build a high-level path planner for use on a drone [13]. The MC controller is capable of moving the drone (shown in Fig. 4) from the ground toward a specific 3D waypoint and maintain a constant height, near that waypoint. The actual position of the waypoint is not prior known, but is detected at run-time using fiducial markers and fed as an input to one of the membranes. Although promising, this advent has also highlighted one of the disadvantages of NPSs, that of execution complexity.

Other research groups have also explored the potential of MC in robot control, most of their applications being based on natuRO’s ENPS (or variants). In [33], trajectory tracking control approach for nonholonomic wheeled mobile robots was approached by using ENPSs. In [34], the problem approached was the multi-objective mobile robot path planning in a dangerous environment with dynamic obstacles, while the solution combined membrane systems with particle swarm optimization. Chapter 6 in [38] is devoted to using NPSs and ENPSs to design MC-based controllers for mobile robots. In [26], a variant of ENPS, called Random Enzymatic Numerical P systems with Proteins and Shared Memory (RENPSM) was used to address the implementation of rapidly exploring random trees (RRT) algorithms to be applied in robot motion planning problems.

3 Limitations, challenges and solutions

Research into the use of MC models for the control of single- or multi-robot systems has offered many insights regarding the design of such models. Nonetheless, there were also challenges and possible bottlenecks that were identified along the way. This section attempts to summarize such limitations and to highlight possible solutions.

Probably, the most important challenge encountered during development was that of memory limitations on embedded systems. This was mostly encountered when working with Pcol/XPcol models on Kilobot robots [9, 11, 15]. These limitations refer both to computational memory (random access memory, RAM) as well as stored program memory. The former is necessary because at the very minimum, an entire Pcol program must be loaded in memory for it to be checked whether it is executable. The latter is also needed to store the entire set of programs and P objects that make up a Pcol. Apart from the memory requirements of the model, there are also those of the Pcol/XPcol simulator that also introduces a considerable overhead [9]. Through careful optimizations, the memory overhead was reduced by 50% but it still remains a stringent restriction for embedded use. One such solution was the compression of P colony programs that contained repetitive rules into a single rule and a marker that specified the number of repetitions of that particular rule. For example, P colonies often employ auxiliary rules such as \(e \rightarrow e\) which can be compressed. During runtime, the process is reversed, by reading the marker and checking the entire program as if it would actually contain the left-out auxiliary rules.

Any memory optimizations have the associated risk of introducing execution time latency. This aspect was also studied and its effects were shown to not always be negative. For instance, although the XPcol model had a larger execution time than the finite state machine model, this difference was not observable for real robots that have a slow movement speed [15]. On the other hand, for applications that require a strict timing, any fluctuations of the execution time of a simulation loop will negatively affect model performance. This was seen for the drone path planner [13], where directly sending pulse width modulation (PWM) signals to the motors at a rate of 500 Hz was proved much too short for an NPS controller that was capable of a loop execution rate of only 100 Hz.

Finally, one last aspect was that of language expressivity where highly complex dependencies between P objects in a P colony had to be expressed using several sequential programs that incrementally prepared an output command from an input value. This meant that the Pcol models were larger and more difficult to review and debug as the flow of information had to be analyzed at each execution step. This problem was also present for NPS models where a complex real-life behavior could only be modeled by adding support for new mathematical functions that can be used to compose new programs.

4 Conclusions and future work

This article presents a summary of the work carried out at natuRO in applying MC-based models to single- and multi-robot systems. New open-source simulators have been introduced that allow the interested researchers to first simulate their controllers based on traditional MC models, such as NPSs, ENPSs, and P colonies. The potential of MC in robot control has been explored in a number of challenging applications over the last 10 years, like the multi-robot (or swarm robotics) control. Research carried out at natuRO has inspired other groups to follow this direction and explore new PSs variants and to explore new applications in robot control. A number of advantages and limitations have been identified and discussed with lots of details in a number of papers.

Example avenues for future related works are as follows.
  1. 1.

    Extending the library of NPSs models with new models that are amenable to more complex robot control applications.

  2. 2.

    Implement these models on parallel computing hardware (such as FPGAs) and so extend the application areas to more complicated robots that need faster reaction times while minimizing FPGA memory resource usage and power consumption.

  3. 3.

    An interesting and much needed development for the whole MC community would be the development of an USB device that brings MC inferencing to existing systems, much like an USB accelerator for machine learning applications.




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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Automatic Control and Systems EngineeringPolitehnica University of BucharestBucharestRomania

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