Abstract
The purpose of this study is to minimize the arc length for the path described by the model of a robot platform when the path is constrained to have smooth transitions given by sigmoid functions. The optimization required a proof of stability for the resulting control law, the selection of the best sigmoid function among ten functions, and the definition of two gains necessary to parameterize the control law. The optimization was carried out by simulating the system under several kinematic and dynamical conditions, and the best sigmoid function was a hyperbolic tangent. Thus, the motion control first implied the simulation of a reference model to define an optimal path, and later the control of an actual robot platform, which followed the optimal path. The use of the optimized path reduced the complexity of the controller while allowing natural and intuitive paths for the robot platform.
Highlights
Path optimization has been a growing area in motion planning for robot platforms
The values of these constants were determined by experimentation; their selection did not result from an optimization process as in the present paper, in which the optimization uses ten sigmoid functions with the goal of minimizing the arc length
This paper proposes a method to choose the best sigmoid function, which consists of setting a path that forces the platform to express a broad dynamic range
Summary
Path optimization has been a growing area in motion planning for robot platforms. Optimization looks for the best route from point A to point B under certain constraints such as energy consumption, speed limits, or obstacle avoidance [1,2,3]. The work in [10] proposes the use of a smooth control law to define the path of a robot instead of limiting the motion planning to define the goal, as in traditional mobile robotics This control strategy divides the kinematics of the model into a fast component that defines the heading angle of the robot and a slow component that sets the forward speed. This paper uses ten sigmoid functions, instead of a single function as in [10], and experimentally looks for every possible kinematic condition for pairs of departure and arrival angles of a platform model, in order to choose the three sigmoid functions that produce the shortest paths These paths require smoother control laws, which in addition prove more intuitive than the paths that result from the application of a traditional PID controller to set a path.
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