Collective transport of arbitrarily shaped objects using robot swarms

Random walks are fundamental search strategies to find an object, particularly when there are no environmental indications, and where walkers lack localization and mapping capabilities [17]. There are many variants of random walks. In two recent independent studies, the ballistic motion variant was reported to result in the broadest area coverage of closed environments [18, 19].

In many ant species, workers cooperate to retrieve large prey that a single ant cannot retrieve. Typically, the ant that finds a prey object first tries to move it. If it remains unsuccessful, it recruits nestmates [12] [p. 256–259]. Like the ants, robotic swarms could work together to retrieve large objects, recruiting sufficient robots. In decentralized collective transport, coordination can be achieved without direct communication, instead relying on coordination through the object being transported [12] [p. 260]. The effect of one agent engaged in collective transport modifies the stimuli perceived by other agents and in turn, produces a change by these agents. This mechanism is known as stigmergy [20].

Other approaches are based on leader–follower principles [21‐23]. In those studies, a leader plans the trajectory and controls the motion, while the remaining robots support the leader’s motion in a coordinated manner. In other approaches, an external supervisor observes the collective motion and sends suitable control actions to the robots to lead the object towards some goal direction [24]. However, these strategies have not been evaluated and generalized to arbitrarily shaped objects. More analytical strategies have also been proposed, but they rely on sophisticated robots that know the object’s shape and position to be transported [25‐27]. As opposed to centralized control approaches, decentralized control approaches are likely to result in suboptimal system performance. However, decentralized strategies have the advantage of being scalable and can be implemented on robots with limited onboard capabilities. The agents only require local information, which they acquire through sensing their environment [28]. Some studies aim to solve the problem of transporting larger objects using robots that can self-assemble into a stronger unit to pull or push an object. Suitable controllers can be synthesized using an evolutionary algorithm [29, 30]. In the work of [6], it was shown that if a number of individual agents apply forces towards the target direction, the object’s center of mass will move in a straight line to the direction of the goal. The versatility of this simple strategy was experimentally demonstrated with up to 100 Kilobot robots [31] collectively transporting numerous complex object shapes. Further, it was noted that the object’s rotational velocity is insignificant compared to its translational velocity. This study provides a valuable example of independently acting robots transporting objects. In this work, we consider distributed robot systems that need to actively lift an object, rather than push it. Unlike with pushing, the risk of instability makes it necessary to reach consensus about when to lift, before attempting a lift. We address this by combining a passive recruitment strategy with a decentralized decision-making process to ensure a coordinated, safe lift and transport.

Experiments were performed in a custom-built agent-based simulator in Python. Robots modeled are omnidirectional, capable of movement in any direction at a speed of 0.2 m/s. The random walk behavior and obstacle avoidance was implemented using a subsumption architecture as introduced by Brooks in [33, 34]. Robots can detect they are under an object and their distance to nearby robots. Further, it is assumed that the robots are equipped with wireless mesh communication technology to communicate with each other.

The swarm’s task is to transport an object to the retrieval area \((2\,\hbox {m} \times 5\,\hbox {m})\) on the side of the area \((7\,\hbox {m} \times 5\,\hbox {m})\), as illustrated in Fig. 1 with an arbitrarily shaped object of size 2 \(\mathrm {m^2}\).

. The robots are initialized with random orientations and at random positions within the warehouse environment, excluding the object’s area. The performance of the collective transport strategy is measured in terms of retrieval time, and number of robots used to transport an arbitrarily shaped object. The retrieval time is defined as the time taken until the robots move the center of the object beyond the vertical dashed line at \(x = 500\, \hbox {cm}\) and into the retrieval area. The maximum time given for the swarm to complete the task is 20 min. The independent variables of the outlined scenario are the swarm size (i.e., the number of deployed robots) and the object’s size. Table 1 shows the simulated parameters for the experimental warehouse setup. These parameters were chosen based on the design of our new swarm for logistics.

As illustrated in Fig. 2, a finite-state machine (FSM) is implemented on the robots to select which behavior(s) to utilize for any given situation.

Figure 3 shows an example simulation of a swarm consisting of 30 agents that collectively retrieve an arrow-shaped object with an area of \(1.26\,\hbox {m}^2\). Important steps are annotated, explaining the collective transport strategy. The three main phases are object search (1a–c), recruitment of sufficient agents for safe lift and transport (2a–c), and collective transport (3a–b).

Positioned agents monitor the state of nearby agents. As the recruitment of agents underneath the object progresses, agents start to fulfill one of the two criteria defined below. The two criteria provide a metric to assess the local arrangement of agents. With this local metric, the aim is to allow the swarm to make a collective decision as to whether there are sufficient agents in place and whether the positioned agents are well-distributed throughout the object. Once all positioned agents have fulfilled either one of the criteria, the swarm collectively decides that it is now safe to lift and transport the object. Table 2 shows the chosen parameters. Note that a smaller number of visited, randomly walking agents would lead to a lift and transport sooner. However, there is a trade-off between ensuring safety and lifting the object in a timely fashion. Choosing the parameters depends on the priority given to safety. Through numerous simulation runs, the parameters were chosen to support a safe lift and transport while also considering the agents’ time to fulfill the criteria.

Once a positioned agent fulfills either of the previously outlined criteria, it changes into the locally safe to lift state, in which the robot initiates a collective lift request. An agent in the locally safe to lift state is ready to lift the object and checks whether all other agents underneath the object are also ready to lift. Each agent that switches into the locally safe to lift state sends out a lift request to all agents underneath this specific object. All agents situated underneath the object respond to the request with either a negative (i.e., locally not ready for a safe lift) or positive (i.e., locally ready for a safe lift) feedback message. This lift request–response communication model is illustrated in Fig. 4.

. If the requesting agent receives one or more negative feedback messages, no lift is initiated. Note that the communication cost increases the larger the object because the lift requesting robot has to communicate with all other robots positioned underneath the object to check their statuses. Finally, once the last agent underneath the object has changed to the locally safe to lift state and has not received any negative feedback, the lift is initiated by a lift command message sent to all involved agents. As a result, all involved agents lift the object in a coordinated fashion and transport it towards the goal direction.

To assess whether sufficient agents lift and transport the object, the number of agents transporting the object was analyzed for each simulation run and summarized for all configurations in Fig. 5.

The horizontal red lines show the minimum number of agents required to feasibly lift and transport an object of a given size. As specified in Table 1 on page 3, every robot can lift a maximum load of 2 kg, and the object is defined to have an equally distributed mass of 8 kg/m\(^2\). Therefore, for example, for a 1.5 m\(^2\) sized object, at least six agents are required for a feasible lift and transport. All simulation runs above those red horizontal lines, also highlighted in green, show scenarios where the object was successfully retrieved with sufficient agents. In the simulation runs highlighted in blue, the object was not lifted and transported because the safe lift and transport criteria were not fulfilled. Respectively, the number of agents transporting the object in these cases was zero.

The safe lift and transport criteria are less likely to be met by all involved agents attempting to safely transport the larger objects because more agents are to be recruited and have to fulfil the criteria within the given time constraint. Also, the number of remaining available robots that assist in fulfilling the object border agents’ safe lift and transport criteria (i.e., Criteria 1) decreases as more robots are positioned underneath the object. To improve the number of cases that result in a successful lift and transport of the larger objects, the proposed method may be enhanced by an active recruitment strategy where already positioned agents actively attract available agents towards the object. Moreover, robots may be equipped with more sophisticated sensing capabilities (e.g., vision system) to identify the object and estimate the number of required agents before moving underneath the object.

Overall, the linear relationship between the object size and the number of agents that decided to lift and transport the object shows the proposed collective transport strategy’s adaptability, reliability and scalability. Given that sufficient agents are deployed and each object has a unique identifier, multiple objects could potentially be transported simultaneously in a fully decentralized fashion.

Figure 6 shows a heatmap of the average time taken for swarms of different sizes to retrieve different sized arbitrarily shaped objects. For the calculation of the average retrieval time, only simulation runs in which the object was retrieved are considered. The grey heatmap entries show swarm and object size pairs that did not result in any completed retrievals within the given 20 min.

Larger swarms generally retrieve objects faster because the object is more likely to be encountered by randomly walking agents. In addition, more agents in the environment help to fulfil the positioned border agents’ safety criteria, leading to an earlier lift and transport of the object. Note that the number of randomly walking agents assisting in fulfilling the positioned border agents’ safety criteria decreases as more agents find and enter underneath the object. Thus, especially for larger objects, swarm size should be increased initially or dynamically on demand.

Altogether, the results show that large and arbitrarily shaped objects can be retrieved both reliably and in a timely fashion, given a large enough swarm size.