Model-based approaches for planning and control for bipedal locomotion have a long history of success. It can provide stability and safety guarantees while being effective in accomplishing many locomotion tasks. Model-free reinforcement learning, on the other hand, has gained much popularity in recent years due to computational advancements. It can achieve high performance in specific tasks, but it lacks physical interpretability and flexibility in re-purposing the policy for a different set of tasks. For instance, we can initially train a neural network (NN) policy using velocity commands as inputs. However, to handle new task commands like desired hand or footstep locations at a desired walking velocity, we must retrain a new NN policy. In this work, we attempt to bridge the gap between these two bodies of work on a bipedal platform. We formulate a model-based reinforcement learning problem to learn a reduced-order model (ROM) within a model predictive control (MPC). Results show a 49% improvement in viable task region size and a 21% reduction in motor torque cost. All videos and code are available at https://sites.google.com/view/ymchen/research/rl-for-roms.

Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM for control captures critical task-relevant aspects of the full dynamics while remaining low dimensional. However, planning within the reduced-order space unavoidably constrains the full model, and hence we sacrifice the full potential of the robot. In the community of legged locomotion, this has lead to a search for better model extensions, but many of these extensions require human intuition, and there has not existed a principled way of evaluating the model performance and discovering new models. In this work, we propose a model optimization algorithm that automatically synthesizes reduced-order models, optimal with respect to a user-specified distribution of tasks and corresponding cost functions. To demonstrate our work, we optimized models for a bipedal robot Cassie. We show in simulation that the optimal ROM reduces the cost of Cassie's joint torques by up to 23% and increases its walking speed by up to 54%. We also show hardware result that the real robot walks on flat ground with 10% lower torque cost. All videos and code can be found athttps://sites.google.com/view/ymchen/research/optimal-rom.

Complex multibody legged robots can have complex rotational control challenges. In this paper, we propose a concise way to understand and formulate a whole-body orientation that (i) depends on system configuration only and not a history of motion, (ii) can be representative of the orientation of the entire system while not being attached to any specific link, and (iii) has a rate of change that approximates total system angular momentum. We relate this orientation coordinate to past work, and discuss and demonstrate, including on hardware, several different uses for it.

State-of-the-art approaches to legged locomotion are widely dependent on the use of models like the linear inverted pendulum (LIP) and the spring-loaded inverted pendulum (SLIP), popular because their simplicity enables a wide array of tools for planning, control, and analysis. However, they inevitably limit the ability to execute complex tasks or agile maneuvers. In this work, we aim to automatically synthesize models that remain low-dimensional but retain the capabilities of the high-dimensional system. For example, if one were to restore a small degree of complexity to LIP, SLIP, or a similar model, our approach discovers the form of that additional complexity which optimizes performance. In this paper, we define a class of reduced-order models and provide an algorithm for optimization within this class. To demonstrate our method, we optimize models for walking at a range of speeds and ground inclines, for both a five-link model and the Cassie bipedal robot.