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Orthogonal Trajectories01:26

Orthogonal Trajectories

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Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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Retraction Note: Reinforcement learning-driven deep learning approaches for optimized robot trajectory planning.

Scientific reportsยท2026
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Reinforcement learning-driven deep learning approaches for optimized robot trajectory planning.

Fang Shiyu1

  • 1Shandong University of Science and Technology, Tai'an, 271019, Shandong, China. fangshiyu250213@163.com.

Scientific Reports
|October 30, 2025
PubMed
Summary

This study integrates deep learning with deep reinforcement learning (DRL) for bipedal robot control. The developed system achieves stable, efficient, and robust walking, even with uncertainties and disturbances.

Keywords:
Bipedal walking robotDeep learningDisturbance rejectionGait pattern generationUncertainty

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Area of Science:

  • Robotics
  • Artificial Intelligence
  • Control Systems

Background:

  • Bipedal walking robots face challenges in stability and efficiency due to complex nonlinear dynamics.
  • Precise joint torque computation is crucial for reliable bipedal locomotion.
  • Deep reinforcement learning (DRL) shows potential for optimizing robot control strategies.

Purpose of the Study:

  • To develop an integrated deep learning and DRL approach for bipedal robot trajectory planning and control.
  • To achieve stable walking with maximum speed, minimal power consumption, and enhanced fall prevention.
  • To improve the robustness and adaptability of bipedal robots under various uncertainties and disturbances.

Main Methods:

  • Integration of deep learning-based trajectory planning with a DRL-driven control system.
  • Training the system to generate optimal joint torque sequences for bipedal locomotion.
  • Testing the robot's performance under mass and length variations, and external disturbances.

Main Results:

  • The trained bipedal robot demonstrated stable and resilient locomotion, maintaining balance throughout the gait cycle.
  • The system exhibited robust performance, handling up to 20% mass variations and 5% length variations.
  • The robot effectively rejected disturbances at various angular velocities and gait phases, showing enhanced adaptability.

Conclusions:

  • The integrated deep learning and DRL approach significantly improves the robustness and efficiency of bipedal robots.
  • This method enhances the reliability and adaptability of bipedal robots for real-world applications.
  • The findings contribute to advancing autonomous locomotion in legged robots.