Designing Tendon-Driven Grippers with Graph Grammar & MCTS

Table of Links

Abstract and I. Introduction

II. Methods

III. Generation of Tendon Driven Grippers

IV. Results and Discussion

V. Conclusion and References

III. GENERATION OF TENDON DRIVEN GRIPPERS

A. Finger design

We simplify the process of optimizing robot component parameters by selecting from a few specific values. The grippers we design consists of the palm and up to four fingers where each finger can have up to five phalanges. The palm serves as the central point of a star topology graph, with each finger branching out as a separate connection. This representation encompasses all mechanisms of a similar nature. Graph grammar rules consist of nodes and edges. The nodes contain all the information, while the edges determine the sequence of details. As a result, each finger consists of three types of nodes: phalanxes, joints and transforms along the palm.

Fig. 4 shows schematic representation of a finger with two phalanges. For each finger algorithm discretely changes base’s position and orientation on a palm, links’ number and their lengths li , spring stiffness ki , and driving force F. The upper and lower bounds for the parameters were manually selected based on the sizes of the objects to be grasped and the components available in the lab, i.e. spring and actuators. We kept the pulley radius constant to simplify the procedure and focus on verifying the general method instead of finding an exact solution.

B. Production rules and robot components

The whole set of production rules is illustrated in Fig. 2. We use terminal and non-terminal nodes in our concept. Non-terminal nodes represent the abstract component which only provides information about the robot’s structure, while terminal nodes represent components with specific physical properties.

The terminal symbols on the scheme represent subsets of terminal nodes. These subsets are used to change the corresponding parameters. For example, the terminal L represents a set of discrete links’ lengths, where each terminal node in the set has its own phalanx size. This graph grammar has two types of rules: (1) type one – changes design morphology, and (2) type two – transforms non-terminal nodes into terminal ones, determining the design parameters.

Even such a simple set allows us to generate vast space of the possible designs, which is another advantage of the graph grammar approach. The design space includes common designs like symmetric two and three finger grippers. It also allows for more unique variations, such as three fingers with different shifts and rotations on one side of the palm, and an

opposing finger on the other side. Fig. 3 shows illustrative example of a sequence of rules that can be applied to generate the simplest one-fingered gripper.

C. Virtual experiment setup

D. Reward function

We designed several quantitative criteria to evaluate the performance of a mechanism in a simulation. Here we present a short description of each criterion.

7) Final reward: A generated gripper gets a scalar reward after each simulation, and we use its value to evaluate the design candidate:

r = w1r1 +w2r2 +w3r3 +w4r4 +w5r5 +w6r6,

where the weight coefficients wi are equal to 1, except w1 = 3, and w6 = 5, because of higher priority. In Fig. 5 samples are given. For example, a reward decomposition for the gripper with the best reward that holds a box is the following

r = 3·1+2·0.31+1·0.36+1·0.96+1·0.77+5·0.95 = 10.46.

We determine the highest value in the control space for each object we grasp. The sum of the highest rewards for all tested objects is then selected as the final reward for the design. Finally, the constructed reward function is used to search the design space applying the MCTS algorithm described in II-C.

8) Remark on reward, bounds and initial state: The weight coefficients in the reward function have a substantial impact on the final designs, along with the initial orientation of objects and the limits set on the structure and parameters. If we limit the number of fingers to the conventional number of three together with limiting the number of phalanges we are getting generic grippers depicted in Fig. 6. From this sense, the main advantage of the proposed procedure is that the algorithm is capable of searching through the vast design space, and what will be the best solution depends on the reward.