Steve Heim

Se Hwan Jeon, Steve Heim, Charles Khazoom et al.

The main challenge in developing effective reinforcement learning (RL) pipelines is often the design and tuning the reward functions. Well-designed shaping reward can lead to significantly faster learning. Naively formulated rewards, however, can conflict with the desired behavior and result in overfitting or even erratic performance if not properly tuned. In theory, the broad class of potential based reward shaping (PBRS) can help guide the learning process without affecting the optimal policy. Although several studies have explored the use of potential based reward shaping to accelerate learning convergence, most have been limited to grid-worlds and low-dimensional systems, and RL in robotics has predominantly relied on standard forms of reward shaping. In this paper, we benchmark standard forms of shaping with PBRS for a humanoid robot. We find that in this high-dimensional system, PBRS has only marginal benefits in convergence speed. However, the PBRS reward terms are significantly more robust to scaling than typical reward shaping approaches, and thus easier to tune.

Jenny Zhang, Steve Heim, Se Hwan Jeon et al.

We present a minimal phase oscillator model for learning quadrupedal locomotion. Each of the four oscillators is coupled only to itself and its corresponding leg through local feedback of the ground reaction force, which can be interpreted as an observer feedback gain. We interpret the oscillator itself as a latent contact state-estimator. Through a systematic ablation study, we show that the combination of phase observations, simple phase-based rewards, and the local feedback dynamics induces policies that exhibit emergent gait preferences, while using a reduced set of simple rewards, and without prescribing a specific gait. The code is open-source, and a video synopsis available at https://youtu.be/1NKQ0rSV3jU.

Felix Grimminger, Avadesh Meduri, Majid Khadiv et al.

We present a new open-source torque-controlled legged robot system, with a low-cost and low-complexity actuator module at its core. It consists of a high-torque brushless DC motor and a low-gear-ratio transmission suitable for impedance and force control. We also present a novel foot contact sensor suitable for legged locomotion with hard impacts. A 2.2 kg quadruped robot with a large range of motion is assembled from eight identical actuator modules and four lower legs with foot contact sensors. Leveraging standard plastic 3D printing and off-the-shelf parts results in a lightweight and inexpensive robot, allowing for rapid distribution and duplication within the research community. We systematically characterize the achieved impedance at the foot in both static and dynamic scenarios, and measure a maximum dimensionless leg stiffness of 10.8 without active damping, which is comparable to the leg stiffness of a running human. Finally, to demonstrate the capabilities of the quadruped, we present a novel controller which combines feedforward contact forces computed from a kino-dynamic optimizer with impedance control of the center of mass and base orientation. The controller can regulate complex motions while being robust to environmental uncertainty.

Chenhao Li, Elijah Stanger-Jones, Steve Heim et al.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

Pierre-François Massiani, Steve Heim, Friedrich Solowjow et al.

Safety constraints and optimality are important, but sometimes conflicting criteria for controllers. Although these criteria are often solved separately with different tools to maintain formal guarantees, it is also common practice in reinforcement learning to simply modify reward functions by penalizing failures, with the penalty treated as a mere heuristic. We rigorously examine the relationship of both safety and optimality to penalties, and formalize sufficient conditions for safe value functions (SVFs): value functions that are both optimal for a given task, and enforce safety constraints. We reveal this structure by examining when rewards preserve viability under optimal control, and show that there always exists a finite penalty that induces a safe value function. This penalty is not unique, but upper-unbounded: larger penalties do not harm optimality. Although it is often not possible to compute the minimum required penalty, we reveal clear structure of how the penalty, rewards, discount factor, and dynamics interact. This insight suggests practical, theory-guided heuristics to design reward functions for control problems where safety is important.

Steve Heim, Alexander von Rohr, Sebastian Trimpe et al.

Failures are challenging for learning to control physical systems since they risk damage, time-consuming resets, and often provide little gradient information. Adding safety constraints to exploration typically requires a lot of prior knowledge and domain expertise. We present a safety measure which implicitly captures how the system dynamics relate to a set of failure states. Not only can this measure be used as a safety function, but also to directly compute the set of safe state-action pairs. Further, we show a model-free approach to learn this measure by active sampling using Gaussian processes. While safety can only be guaranteed after learning the safety measure, we show that failures can already be greatly reduced by using the estimated measure during learning.

Steve Heim, Alexander Spröwitz

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.

Steve Heim, Alexander Spröwitz

Despite impressive results using reinforcement learning to solve complex problems from scratch, in robotics this has still been largely limited to model-based learning with very informative reward functions. One of the major challenges is that the reward landscape often has large patches with no gradient, making it difficult to sample gradients effectively. We show here that the robot state-initialization can have a more important effect on the reward landscape than is generally expected. In particular, we show the counter-intuitive benefit of including initializations that are unviable, in other words initializing in states that are doomed to fail.

Steve Heim, Felix Ruppert, Alborz A. Sarvestani et al.

Learning instead of designing robot controllers can greatly reduce engineering effort required, while also emphasizing robustness. Despite considerable progress in simulation, applying learning directly in hardware is still challenging, in part due to the necessity to explore potentially unstable parameters. We explore the concept of shaping the reward landscape with training wheels: temporary modifications of the physical hardware that facilitate learning. We demonstrate the concept with a robot leg mounted on a boom learning to hop fast. This proof of concept embodies typical challenges such as instability and contact, while being simple enough to empirically map out and visualize the reward landscape. Based on our results we propose three criteria for designing effective training wheels for learning in robotics. A video synopsis can be found at https://youtu.be/6iH5E3LrYh8.