SmoothTurn: Learning to Turn Smoothly for Agile Navigation with Quadrupedal Robots

Abstract

Quadrupedal robots show great potential for valuable real-world applications such as fire rescue and industrial inspection. Such applications often require urgency and the ability to navigate agilely, which in turn demands the capability to change directions smoothly while running in high speed. Existing approaches for agile navigation typically learn a single-goal reaching policy by encouraging the robot to stay at the target position after reaching there. As a result, when the policy is used to reach sequential goals that require changing directions, it cannot anticipate upcoming maneuvers or maintain momentum across the switch of goals, thereby preventing the robot from fully exploiting its agility potential. In this work, we formulate the task as sequential local navigation, extending the single-goal-conditioned local navigation formulation in prior work. We then introduce SmoothTurn, a learning-based control framework that learns to turn smoothly while running rapidly for agile sequential local navigation. The framework adopts a novel sequential goal-reaching reward, an expanded observation space with a lookahead window for future goals, and an automatic goal curriculum that progressively expands the difficulty of sampled goal sequences based on the goal-reaching performance. The trained policy can be directly deployed on real quadrupedal robots with onboard sensors and computation. Both simulation and real-world empirical results show that SmoothTurn learns an agile locomotion policy that performs smooth turning across goals, with emergent behaviors such as controlling momentum when switching goals, facing towards the future goal in advance, and planning efficient paths. We have provided video demos of the learned motions in the supplementary materials. The source code and trained policies will be made available upon acceptance.

Figures (4)

• Figure 1: Composited images of SmoothTurn deployed on a Unitree Go2 performing agile navigation in an indoor office environment. The learned policy enables the robot to maintain momentum and high speed while executing turns rapidly through corridors and corners.
• Figure 2: Overview of the SmoothTurn framework. The Goal Sampler generates a sequence of segment goals based on the curriculum. The Command Updater advances the goal index upon goal reaching and provides the pose of current and future goals in the robot base frame. The Policy takes the commands and proprioceptive states as input to output joint position targets.
• Figure 3: Example trajectories colored by the instantaneous base linear velocity magnitude (m/s) on the four goal sequences. The goals in the sequences are labeled by the blue arrows.
• Figure 4: Reward curves of SmoothTurn and its variants under relaxed goal-reaching conditions when the robot is commanded to complete the 90º (CCW) goal sequence, with robots motions at some key moments labeled. Frames 1-3 are from SmoothTurn, frames 4-6 are from SmoothTurn ($\epsilon_{\theta} = +\infty$), frames 7-9 are from SmoothTurn ($\epsilon_{xy} = 0.5$).