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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.

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Multi agent system is a system consist of multiple interacting agents. These systems tend to select the best solution for their problems. They can be used in different tasks which are hard for an individual or even a complex system to do. One of the most common algorithms which are used in multi agent systems is flocking. Here we introduce a theorem that multi agent systems could flock in environments with fixed obstacles without any collision between agents and obstacles. We use lyapunov theory and prior algorithms on flocking to extract a theorem which under those conditions in the theorem, collision never occurs between agents and obstacles. Results show that the theorem insures collision avoidance between agents and obstacles.