Non-contact robotic manipulation of floating objects: exploiting emergent limit cycles

Abstract

The study of non-contact manipulation in water, and the ability to robotically control floating objects has gained recent attention due to wide-ranging potential applications, including the analysis of plastic pollution in the oceans and the optimization of procedures in food processing plants. However, modeling floating object movements can be complex, as their trajectories are influenced by various factors such as the object's shape, size, mass, and the magnitude, frequency, and patterns of water waves. This study proposes an experimental investigation into the emergence ofrobotically controlled limit cycles in the movement of floating objects within a closed environment. The objects' movements are driven by robot fins, and the experiment plan set up involves the use of up to four fins and variable motor parameters. By combining energy quantification of the system with an open-loop pattern generation, it is possible to demonstrate all main water-object interactions within the enclosed environment. A study using dynamic time warping around floating patterns gives insights on possible further studies.

Keywords: floating objects; limit cycles; non-contact manipulation; ocean engineering; water interactions.

FIGURE 1

Experiment setup for this study, with the 4 fin setups in the corners (A), selected floating objects with dimensions (B), motor and fin system placed in corners, which allows only for rotation in around the rod axis (C), and parameterized controller plot according to standard motor parameters (D).

FIGURE 2

(A) Top view of the floating objects’ cross section with the calculated radius at the water surface. (B) Side view of the floating objects with the submerged distance and volume indicated.

FIGURE 3

Standard patterns for the puck and the ball (Amplitude = 70°, Pause time = 0.8 s). In both scenario, the fin is actuated for 45 s, then the system is allowed to decay freely in energy for the next 10 s. The loop dimensions in the bottom right corner is related to the object’s geometrical properties.

FIGURE 4

Maximum free displacement after a single back and forth fin stroke for the ball and the puck. The ball reacts periodically to stroke amplitudes, while the puck behave like a band-pass filter. For this plot, each sequence is performed 15 times with clear outliers (due to tracking errors) removed.

FIGURE 5

Experiment plan results for a single motor setup - Start position in front of the fin. From left to right: Standard parameters, lower amplitude, longer pause time, higher amplitude and longer pause time. Each sequence is repeated 5 times with similar parameters. Green and red frames around each sub-figure are indicative markers of the presence or absence of limit cycles.

FIGURE 6

Normalized distance found by Dynamical Time Warping, between the trajectories for limit cycles with a single motor (Figure 5) and a representative trajectory. Blue bars are related to the Puck, while orange bars are related to the Ball. Excluding the final results A = 70° and t _p = 0.2 s, the normalized energy is consistently lower for the ball as compared to the puck. DTW is therefore a valid way to sort objects based on their energy.

FIGURE 7

Experiment results for a dual motor setup—Start position in the middle of the system. From left to right: Standard parameters, lower amplitude, longer pause time, higher amplitude and longer pause time. Each sequence is repeated 5 times with similar parameters. Green and red frame are indicative markers of the presence or absence of limit cycles.

FIGURE 8

Paths in open loop following Z-shaped (A) and inverted L-shaped (C) pattern with the corresponding motor sequence (B) and (D), respectively. Motor sequences are a subtle mix of motor order, with motor sweep amplitude and pause time. The two open-loop patterns are fully repeatable between the top two motors. The trajectory is then heavily influenced by how the object catches the waves coming from the top right fin (motor #1).

FIGURE 9

Surface tension of objects in contact with the walls. When the object becomes wet and comes into contact with a wall, surface tension tends to cause it to adhere to the panel inversely proportional to the body’s weight. The ball is therefore more prone to this phenomenon.