Many different control schemes have been proposed in the technical literature to control the special class of underactuated systems, the- so-called brachiation robots. However, most of these schemes are limited with regard to the method by which the robot executes the brachiation movement. Moreover, many of these control strategies do not take into account the energy of the system as a decision variable. To observe the behavior of the system’s, energy is very important for a better understanding of the robot dynamics while performing the motion. This paper discusses a variety of energy-based strategies to better understand how the system’s energy may influence the type of motion (under-swing or overhand) the robot should perform.

The control of a brachiation robot has been the primary objective of this study. A brachiating robot is a type of a mobile arm that is capable of moving from branch to branch similar to a long-armed ape. In this paper, to minimize the actuator work, Pontryagin's minimum principle was used to obtain the optimal trajectories for two different problems. The first problem considers “brachiation between fixed branches with different distance and height,” whereas the second problem deals with the “brachiating and catching of a moving target branch”. Theoretical results show that the control effort in the proposed method is reduced by 25% in comparison with the “target dynamics” method which was proposed by Nakanishi et al. (1998)16 for the same type of robot. As a result, the obtained optimal trajectory also minimizes the brachiation time. Two kinds of controllers, namely the proportional-derivative (PD) and the adaptive robust (AR), were investigated for tracking the proposed trajectories. Then, the previous method on a set-point controller for acrobat robots is improved to represent a new AR controller which allows the system to track the desired trajectory. This new controller has the capability to be used in systems which have uncertainties in the kinematic and dynamic parameters. Finally, theoretical results are presented and validated with experimental observations with a PD controller due to the no chattering phenomenon and small computational efforts.