# Robotic Assembly for Irregular Shaped Peg-in-Hole with Partial Constraints
## 1 Introduction  
Automatic assembly is an important part of an industrial automation system. The robot, due to its high flexibility, plays a key role in the fully automatic assembly system. However, in a typical assembly task, the workpieces have to contact each other in order to accomplish the mating process. Therefore, different from material handling, welding or spraying tasks, the robotic assembly not only requires precisely controlling the robot position but also needs to regulate the contact force compliantly and safely. Therefore, complex hybrid control policies have to be designed according to different configurations. Peg-in-hole is one of the most common operations in assembly applications. Because of the limitations on the robot repeatability, fixturing and grabbing errors, the tight tolerant peg-in-hole task used to be a difficult task [1]. Without compliant control policy, the initial errors may generate huge reaction force, which may damage the robot or workpieces. Without a sophisticated control policy, the success rate will be low for large variation scenarios. Passive compliance and active compliance are two ways to implement the compliance peg-in-hole operation. The passive compliance uses a flexible device like a rubber spring to link the end effector and gripper. The error will be compensated by the device's deformation [1; 2; 3]. However, the passive compliance device is not generally applicable and has to be redesigned according to different task configurations. With the development of force sensors, the active force control is more and more used in many applications. The force sensor is installed at the end effector to detect the contact force. This force information isthen regarded as the feedback for the close loop control system. The controller regulates the posture/force/impendence parameters to reduce the contact force and realize the compliance behavior [4; 5]. According to the shape of the peg, the tasks can be classified into cylinder peg-in-hole assembly and irregular shaped peg-in-hole assembly [6]. According to the number of pegs, it can be classified into single peg-in-hole and multiple peg-in-hole tasks [7]. According to the stages of the peg, it can be classified into single stage peg-in-hole and cascaded peg-in-hole assembly [8]. Most studies focus on cylinder peg-in-hole tasks. Error compensation and search-insertion strategies are widely used to accommodate peg position and rotation errors. Spiral, circular, or line search patterns are commonly used to efficiently search for the real hole position. For irregular shaped peg-in-hole tasks, such as square peg and key-slot assembly, the above 2 DOF search method becomes inefficient because the search space changes from 2 to 3. There are two categories of peg-in-hole assembly strategies: model-based and model-free methods [9]. Model-based methods use a prebuilt force/geometric model to map the force measurement to geometric errors and then use this prediction to compensate for the part position/posture errors. Some papers use the exact mathematic model to find the properly compliant assembly strategies. [PERSON] built a three point contact model to estimate the tilt angle to complete autonomous error correction and insertion [10]. [PERSON] proposed a geometrical model to improve the efficiency and robustness in the tight tolerance peg-hole insertion [11]. Some studies use the contact-model to avoid collisions and reduce jamming. [PERSON] proposed a jamming reduced method through the mathematical model analysis of peg-in-hole assembly [12; 13]. [PERSON] analyzed point contact and face contact situation of the peg-in-hole assembly and proposed screw insertion strategies to reduce friction [14]. Model-free methods require no geometric or force model but directly map the force measurement to some behavior or an open-loop control strategy. The model-free method is an implicit method which is used to avoid complex computing process and make the robot to directly complete the assembly operation.