# Model-Based Design and Evaluation of a Brachiating Monkey Robot with an Active Waist
## 1 Introduction  
While most legged animals move on the ground by using their legs when walking [1], running [2; 3], leaping [4], or crawling [5], a special subset of legged animals includes primates who have a different kind of locomotion mechanism owing to the characteristics of the habitat. Monkeys live in trees, which can be regarded as a special kind of terrain that is scattered and randomly distributed in all directions. Thus, using arms for locomotion, or so called brachiation, has naturally evolved in primates such as gibbons and siamangs. Their brachiation mechanism has been studied [6; 7], and the influence of their size and proportion on biomechanic characteristics have been reported as well [8]. Brachiation locomotion acts as a unique class of limbed locomotion that can negotiate some types of special terrain, where other methods may not be functional. Continuous brachiation locomotion in general is composed of a swing motion with respect to a fixed point and the change of fixed points for forward motion. Because the fixed point is usually above the system, the swing motion is similar to that of a pendulum [9; 10]. The dynamics of a multi-link pendulum with respect to a fixed position have been well studied, especially for the two-link [11; 12; 13; 14; 15] and the three-link [16; 17] systems, as acrobatic motion performed by gymnasts can also be modeled in this manner [18]. The research topics have included the pendulum focus on energy transformation mechanism, control strategy, and parameter identification. Most studies have been conducted in a simulation environment, and some have produced experimental results [13; 16]. In addition to the study of pendulum dynamics, some research has focusedon the change in fixed positions in the performance of complete brachiation locomotion. Similarly, two-link [19; 20; 21; 22; 23; 24; 25; 26] and three-link [27; 28; 29; 30] systems have been widely adopted. In these studies, different controllers were applied and simulated to stabilize the behavior and to reject disturbances, and some studies included comparisons between simulations and experimental results [21; 24; 29]. The empirical robots in this category needed to have extra degrees-of-freedom (DOFs) to grasp/release or switch the fixed positions, and a distance sensor was used to detect the distance and height of the bars for brachating adjustment [31]. Later, the simulation studies used models with link numbers up to seven to simulate the complex dynamics of primates [32; 33; 34; 35; 36]. In our study, we report on the simulation and experimental results of a monkey robot in brachiation locomotion. Unlike other studies where the models/robots grasp the fixed bar, we intend to investigate the behavior while the robot grasps a swingable rod, as the intermediate step toward studying brachiation on the soft rope. The system, which is composed of the robot and the rope/rod, has a more concentrated mass/size distribution and a larger distance to the fixed end (i.e., the top of the rope/rod) than the system composed of the robot and a fixed bar, as reported in other literature. Thus, the mechanical property of the rope/rod changes the overall system dynamics, and the passive rope/rod enlarges the swing amplitude of the robot as well as increases the possibility of catching. Following this setup, the two-step control strategy is developed, so the system can initiate the swing motion from rest as well as maintain the swing with a large amplitude. The system is modeled and the empirical robot is built and experimentally evaluated. The remainder of the paper is organized as follows. Note that the motivation of this work is neither the development of a sophisticated control strategy of the two-link pendulum nor the development of a complex robot to mimic the monkey itself. Instead, we focus on how to design a simple robot and to simultaneously find a corresponding simple model (i.e., template vs. anchor [37]), so the complex brachating behavior of the monkey can be abstractly reconstructed.