Online Planning of Adaptive Locomotion

While legged robots are physically suited for traversing challenging terrain, it is computationally costly to plan adaptive locomotion that anticipates upcoming obstacles. We are developing a framework to generate and sustain such behavior online by combining trajectory optimization and machine learning. Our optimization formulation promotes robustness and enables receding horizon deployment while relaxing assumptions about the manner in which the problem is solved. To minimize the required computation we initialize the optimizer with high-quality guesses from a deep neural network, which is trained on an expert dataset using a special scheme to cope with its multimodal nature. For details, please see our papers listed below.

ICRA 2021: Receding-Horizon Perceptive Trajectory Optimization for Dynamic Legged Locomotion with Learned Initialization

Abstract: To dynamically traverse challenging terrain, legged robots need to continually perceive and reason about upcoming features, adjust the locations and timings of future footfalls and leverage momentum strategically. We present a pipeline that enables flexibly-parametrized trajectories for perceptive and dynamic quadruped locomotion to be optimized in an online, receding-horizon manner. The initial guess passed to the optimizer affects the computation needed to achieve convergence and the quality of the solution. We consider two methods for generating good guesses. The first is a heuristic initializer which provides a simple guess and requires significant optimization but is nonetheless suitable for adaptation to upcoming terrain. We demonstrate experiments using the ANYmal C quadruped, with fully onboard sensing and computation, to cross obstacles at moderate speeds using this technique. Our second approach uses latent-mode trajectory regression (LMTR) to imitate expert data—while avoiding invalid interpolations between distinct behaviors—such that minimal optimization is needed. This enables high-speed motions that make more expansive use of the robot’s capabilities. We demonstrate it on flat ground with the real robot and provide numerical trials that progress toward deployment on terrain. These results illustrate a paradigm for advancing beyond short-horizon dynamic reactions, toward the type of intuitive and adaptive locomotion planning exhibited by animals and humans.


  • “Receding-Horizon Perceptive Trajectory Optimization for Dynamic Legged Locomotion with Learned Initialization”, Oliwier Melon, Romeo Orsolino, David Surovik, Mathieu Geisert, Ioannis Havoutis, Maurice Fallon, IEEE Intl. Conf. on Robotics and Automation (ICRA), 2021.

CoRL 2020: Learning an Expert Skill-Space for Replanning Dynamic Quadruped Locomotion over Obstacles

Abstract: Function approximators are increasingly being considered as a tool for generating robot motions that are temporally extended and express foresight about the scenario at hand. While these longer behaviors are often necessary or beneficial, they also induce multimodality in the decision space, which complicates the training of a regression model on expert data. Motivated by the problem of quadrupedal locomotion over obstacles, we apply an approach that disentangles modal variation from task-to-solution regression by using a conditional variational autoencoder. The resulting decoder is a regression model that outputs trajectories based on the task and a real-valued latent mode vector representing a style of behavior. With the task consisting of robot-relative descriptions of the state, the goal, and nearby obstacles, this model is suitable for receding-horizon generation of structured dynamic motion. We test this approach, along with a trajectory library baseline method, for producing sustained locomotion plans that use a generalized gait. Both options strongly bias planned footholds away from obstacle regions, while the multimodal regressor is far less susceptible to violating kinematic constraints. We conclude by identifying further prospective benefits of the continuous latent mode representation, along with targets for future integration into a hardware-deployable pipeline including perception and control.


  • “Learning an Expert Skill-Space for Replanning Dynamic Quadruped Locomotion over Obstacles”, David Surovik, Oliwier Melon, Mathieu Geisert, Maurice Fallon, Ioannis Havoutis, Conf. on Robot Learning, 2020.

ICRA 2020: Reliable Trajectories for Dynamic Quadrupeds using Analytical Costs and Learned Initializations

Abstract: Dynamic traversal of uneven terrain is a major objective in the field of legged robotics. The most recent model predictive control approaches for these systems can generate robust dynamic motion of short duration; however, planning over a longer time horizon may be necessary when navigating complex terrain. A recently-developed framework, Trajectory Optimization for Walking Robots (TOWR), computes such plans but does not guarantee their reliability on real platforms, under uncertainty and perturbations. We extend TOWR with analytical costs to generate trajectories that a state-of-the-art whole-body tracking controller can successfully execute. To reduce online computation time, we implement a learning-based scheme for initialization of the nonlinear program based on offline experience. The execution of trajectories as long as 16 footsteps and 5.5 s over different terrains by a real quadruped demonstrates the effectiveness of the approach on hardware. This work builds toward an online system which can efficiently and robustly replan dynamic trajectories.


  • “Reliable Trajectories for Dynamic Quadrupeds using Analytical Costs and Learned Initializations”, Oliwier Melon, Mathieu Geisert, David Surovik, Ioannis Havoutis, Maurice Fallon, IEEE Intl. Conf. on Robotics and Automation (ICRA), 2020.