Controlling Ant-like Robots to Collectively Navigate through Obstacles

By Jillian Kunze

Teams of small robots that work collectively to navigate and transport objects have many useful applications; search and rescue after disasters, construction in uncertain environments, and planetary exploration comprise just a few. But these robot teams need a control framework within which they can navigate harmoniously together. During a minisymposium presentation at the 2021 SIAM Conference on Applications of Dynamical Systems, which is taking place virtually this week, Hamed Farivarnejad of Arizona State University presented his joint work with advisor Spring Berman to design controllers for ant-like robots to collectively convey an object to a destination. 

“Collective transport in ants is a striking example,” Farivarnejad said. When ants work together to transport objects back to their nest, they have no explicit communication, no predefined paths for their motion, and no sense of their position on a global scale. They also do not know many details about their payload’s dynamics or the distribution of their fellow ants around it, and they may not have any prior knowledge of the shapes and positions of the obstacles they will encounter. The ants only know the direction to their nest, and are able to use only local measurements of their surroundings to navigate there. The researchers hoped to mimic these abilities in this study. 

Much prior work on collective transport has focused on leader-follower control, in which one or more leaders tell their followers where to go. But this strategy is vulnerable to a leader’s failure and requires the leader have predefined trajectories for the motion, as well as information about the payload’s dynamics and geometry, which is not always feasible in an uncertain situation. Other work has focused on decentralized controllers for a team of multiple identical robots, but still needed a predefined trajectory along with a lot of outside information about the payload.

Farivarnejad and Berman intended to use much less information to direct collective transport. The researchers aimed to develop a mathematical control law for multiple miniscule robots that are located around the perimeter of an object and must transport it to a predetermined target, but have no predefined trajectory. The robots all have identical capabilities, and do not know anything about the dynamics and geometry of their payload nor the distribution of their team around it. They also have no prior knowledge of the location and shape of obstacles, and cannot explicitly communicate with each other. These robots can only access local measurements of their surroundings and their global position as they attempt to transport their payload to the target position without colliding with or getting stuck between any obstacles. “For sensing, the main assumption was that there was only localization,” Farivarnejad said. “The robots had access to only their own properties, location, and distance to obstacles.”

Farivarnejad described several mathematical tools relevant to the design and analysis of the controller for the robots: a proportional-derivative control law defined the robots’ movement, and LaSalle’s invariance principle showed that the possible trajectories the robots could take would converge to a certain set. The steady-state error—i.e., the distance between the payload and the goal position as the robots reach the end of their movement—is a function of the number of robots and their distribution around the payload. 

The researchers first attempted several simulations of their new controller with different distributions of six robots around a circular payload, not yet including any obstacles. In their first try, the robots were equally spaced around the payload and were able to move straight to the goal position (see Figure 1). In the second simulation, the robots were not distributed uniformly, and in the third, the robots were clustered within a quarter of the payload’s perimeter. Unsurprisingly, the steady state error became larger as the distribution of the robots became less uniform. 

The next step was to model the navigation of a single robot through obstacles, under the same conditions and with the same goals as they were aiming for the collective ant-like robots. To do so, the researchers drew inspiration from the navigation functions that Daniel E. Koditschek and Elon Rimon introduced in 1990. Those functions require very accurate information about any obstacles. But Farivarnejad described how they relaxed those restrictions to create what he called navigation-like functions, since the context of this work is that the robot knows nothing about the obstacles besides what it can sense in the moment. 

In order to introduce these navigation-like functions, Farivarnejad defined separate kinds of functions for the repulsion spaces around obstacles and the safe spaces that were suitably far away from any impedance (see Figure 2). He then defined a control law for the robot based on these spaces. “The robot requires only its local measurement to calculate the control law,” he said. Simulations showed that the robot was able to reach its target when operating with this controller, even if it started and ended in a repulsion space.

Farivarnejad then extended these results to the collective transport of a payload by multiple minute robots. This again required defining a new control law that depended on the position of each robot and its distance from any obstacles nearby. The simulation results once more showed successful transport of the payload to the target location in multiple scenarios (see Figure 3). 

There still remains further work to guarantee that the robots will never collide with obstacles or get the payload stuck. In the future, Farivarnejad also hopes to further restrict the position control of collective transport so that the robots do not know their global position, and regulate the internal forces applied to the payload to ensure that the robots never pull it apart. These steps could be important for applying the control laws for robot teams in real-world uncertain environments.

Jillian Kunze is the associate editor of SIAM News.