<p>This article presents the application of the Soft Actor-Critic algorithm to balance an underactuated biped robot on a single leg and analyzes its effectiveness, which has not been previously explored. A five-link biped robot is modeled using a multibody dynamic approach, incorporating a unilateral joint constraint about the point foot. As the robot is an unactuated ankle, joint torques at the hip and knee, as well as foot ground friction, play a crucial role in maintaining the balance by ensuring the static friction remains within the friction cone. This paper considers a point-footed robot with actuators at the hip and knee joints only and employs a Soft Actor-Critic reinforcement learning approach to find stable postures or geometrical configurations. The robot configurations, friction, and reaction forces are part of the observation space for the neural network inputs. The neural network outputs represent the action space, requiring torque at the hips and knees for balancing. This study shows that underactuated biped robots can maintain different postures for the varying coefficients of friction, ranging from <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1782_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mu = 0.441\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.441</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1782_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mu = 0.0.780\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.0</mn> <mo>.</mo> <mn>780</mn> </mrow> </math></EquationSource> </InlineEquation>. This article also demonstrates that the proposed model can reject external disturbance in the form of an impulse 10 N force for (10&#xa0;ms), 5 N force for (10&#xa0;ms), 2 N force for (50&#xa0;ms), and 1 N force for (80&#xa0;ms) at <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1782_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu = 0.611\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.611</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Learning to balance: reinforcement learning control for single-leg balance of an underactuated biped robot

  • Krishna Prakash Yadav,
  • Jyotindra Narayan,
  • Prabhakar Kushwaha

摘要

This article presents the application of the Soft Actor-Critic algorithm to balance an underactuated biped robot on a single leg and analyzes its effectiveness, which has not been previously explored. A five-link biped robot is modeled using a multibody dynamic approach, incorporating a unilateral joint constraint about the point foot. As the robot is an unactuated ankle, joint torques at the hip and knee, as well as foot ground friction, play a crucial role in maintaining the balance by ensuring the static friction remains within the friction cone. This paper considers a point-footed robot with actuators at the hip and knee joints only and employs a Soft Actor-Critic reinforcement learning approach to find stable postures or geometrical configurations. The robot configurations, friction, and reaction forces are part of the observation space for the neural network inputs. The neural network outputs represent the action space, requiring torque at the hips and knees for balancing. This study shows that underactuated biped robots can maintain different postures for the varying coefficients of friction, ranging from \( \mu = 0.441\) μ = 0.441 to \( \mu = 0.0.780\) μ = 0.0 . 780 . This article also demonstrates that the proposed model can reject external disturbance in the form of an impulse 10 N force for (10 ms), 5 N force for (10 ms), 2 N force for (50 ms), and 1 N force for (80 ms) at \(\mu = 0.611\) μ = 0.611 .