Modeling of novel circular gait motion through daisy sequence fitting algorithm in a vertical climbing snake robot
Problem Statement:
A snake robot used in climbing trees and cutting parts of tress be it branches or fruits. Also, since snake robot is a redundant manipulator, it can be used to to climb and do surveillance of the environment. But for this purpose, with the existing gait motions and techniques, it requires more torque which increases the weight and power requirement as well. This creates a difficult situation to control the snake robot using controllers while it is cutting the parts of the tree.
Goal:
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To come up with gait motion that enables the snake robot to move around the tree in a horizontal plane with low torque requirements, hence low power consumption
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To implement a suitable controller for the desired gait motion
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Validate the proposed motion and generate results in terms of response characteristics
Approach:
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Conceptualizing the circular gait motion by modelling as lifting a set of modules of snake robot at each time
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Calculating the torque requirement if the modules were to act as arm stretching to cut the tree parts
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Creating the backbone curves and keyframes for the conceptualized circular gait motion around the tree
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Devising fitting algorithm that fit's the module's center of mass to the created backbone curve using DH parameters
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Implementing control systems & carrying out comparisons between controllers with their performance for the gait
Results:
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The backbone curve with EO (target) points are created as shown below
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To fit the module to the backbone curve, Daisy sequence fitting algorithm is devised which uses gradient decent optimization and DH parameter to fit modules individually to the curve.
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The objective function is in terms of distance between module's center of mass and back bone curve's corresponding EO point as
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The joint angles of modules are plotted as shown in fig 12. if the time step is increased, a smooth half sine wave curve will be obtained with 90 phase difference between the adjacent modules.
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The response of joint angles vs time is shown in fig 14 for a Sliding mode (SM) controller. Fig 15(c) shows the response of the PID controller. Since, the current and actual position of each module overlaps more for the SM controller, it is selected as the versatile controller for the intended application
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The torque requirement is validated for two cases:
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case 1:
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In order to obtain various perspectives for observation, the snake robot climbs the tree (stage 1) and raises four of its modules (stage 2). The torque graph for each module in relation to simulation time is displayed in Figure 16a. The snake robot passes through stage 1 of the simulation, which involves performing the standard rolling gait, for up to 3.5 seconds. Subsequently, four modules are raised in a cantilever orientation to provide an additional perspective of the surroundings. Modules J5 and J7 needed a torque of roughly 8 N m to be in this stable position. ​
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case 2:
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The snake robot executes the same gait as in stage 1 and after this it executes the devised circular gait motion (stage 2). All modules are able to perform the circular gait motion within the 4.5 Nm torque limit, as shown in Figure 16b. Stage is up to 4.5 seconds in Figure 16b. Following that, the circular gait motion is carried out, during which the torque of the module varies between 4.5 Nm torque. Hence low torque surveillance and cutting applications after tree climbing is achieved. ​
Robot Full motion Visualization:
In fig 8(a), we can see that the snake robot clings to the tree/pole and starts the climbing (rolling) motion. After climbing the pole in fig 8(b), the snake robot starts the circular gait motion which makes the entire snake robot to rotate on a horizontal plane about the pole as the center. This is understood by understanding the End Effector(EE) position in fig 8(b) and fig (c). In fig 8(b) EE is on the left side of the pole and it has moved behind the tree and reached the position on the right side of the pole as seen in fig 8(c) on the same height level.