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Fix a typo
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report/report.tex

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The servo control library used for this project allows motor targets to be set with single-degree precision, so a single joint can have integer positions in $[0\degree, 155\degree]$. For each configuration, the LED can be either on or off, so there are a total of 48050 states. At a given time step, the agent may choose to keep a joint fixed, move it left, or move it right and it can choose to activate or deactivate the LED. Assuming we restrict the agent to movements of unit magnitude, this means there are 18 actions.
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A state-action value table based on this representation, assuming 4 byte floats, would occupy more than 4 megabytes of memory. Due to the spread of the light of the LED, it may be feasible to reduce the fidelity of the joint state representation and still achieve good performance, and because the optimal policy will likely always elect to move a joint, we may be able to remove actions which do not move a joint with little adverse effect. Even then, the microcontroller could only theoretically fit 10\% of all state action pairs (less without careful optimization, as the stack needs to live in memory as well). A tabular approach is not feasible due to the system's memory contraints.
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A state-action value table based on this representation, assuming 4 byte floats, would occupy more than 4 megabytes of memory. Due to the spread of the light of the LED, it may be feasible to reduce the fidelity of the joint state representation and still achieve good performance, and because the optimal policy will likely always elect to move a joint, we may be able to remove actions which do not move a joint with little adverse effect. Even then, the microcontroller could only theoretically fit 10\% of all state action pairs (less without careful optimization, as the stack needs to live in memory as well). A tabular approach is not feasible due to the system's memory constraints.
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\subsubsection{Function Approximation}
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\end{center}
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\end{document}
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\end{document}

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