DTC: Deep Tracking Control.

Legged locomotion is a complex control problem that requires both accuracy and robustness to cope with real-world challenges. Legged systems have traditionally been controlled using trajectory optimization with inverse dynamics. Such hierarchical model-based methods are appealing because of intuitive cost function tuning, accurate planning, generalization, and, most importantly, the insightful understanding gained from more than one decade of extensive research. However, model mismatch and violation of assumptions are common sources of faulty operation. Simulation-based reinforcement learning, on the other hand, results in locomotion policies with unprecedented robustness and recovery skills. Yet, all learning algorithms struggle with sparse rewards emerging from environments where valid footholds are rare, such as gaps or stepping stones. In this work, we propose a hybrid control architecture that combines the advantages of both worlds to simultaneously achieve greater robustness, foot-placement accuracy, and terrain generalization. Our approach uses a model-based planner to roll out a reference motion during training. A deep neural network policy is trained in simulation, aiming to track the optimized footholds. We evaluated the accuracy of our locomotion pipeline on sparse terrains, where pure data-driven methods are prone to fail. Furthermore, we demonstrate superior robustness in the presence of slippery or deformable ground when compared with model-based counterparts. Last, we show that our proposed tracking controller generalizes across different trajectory optimization methods not seen during training. In conclusion, our work unites the predictive capabilities and optimality guarantees of online planning with the inherent robustness attributed to offline learning.

Versatile multicontact planning and control for legged loco-manipulation.

Loco-manipulation planning skills are pivotal for expanding the utility of robots in everyday environments. These skills can be assessed on the basis of a system's ability to coordinate complex holistic movements and multiple contact interactions when solving different tasks. However, existing approaches have been merely able to shape such behaviors with hand-crafted state machines, densely engineered rewards, or prerecorded expert demonstrations. Here, we propose a minimally guided framework that automatically discovers whole-body trajectories jointly with contact schedules for solving general loco-manipulation tasks in premodeled environments. The key insight is that multimodal problems of this nature can be formulated and treated within the context of integrated task and motion planning (TAMP). An effective bilevel search strategy was achieved by incorporating domain-specific rules and adequately combining the strengths of different planning techniques: trajectory optimization and informed graph search coupled with sampling-based planning. We showcase emergent behaviors for a quadrupedal mobile manipulator exploiting both prehensile and nonprehensile interactions to perform real-world tasks such as opening/closing heavy dishwashers and traversing spring-loaded doors. These behaviors were also deployed on the real system using a two-layer whole-body tracking controller.

Constrained stochastic optimal control with learned importance sampling: A path integral approach.

Modern robotic systems are expected to operate robustly in partially unknown environments. This article proposes an algorithm capable of controlling a wide range of high-dimensional robotic systems in such challenging scenarios. Our method is based on the path integral formulation of stochastic optimal control, which we extend with constraint-handling capabilities. Under our control law, the optimal input is inferred from a set of stochastic rollouts of the system dynamics. These rollouts are simulated by a physics engine, placing minimal restrictions on the types of systems and environments that can be modeled. Although sampling-based algorithms are typically not suitable for online control, we demonstrate in this work how importance sampling and constraints can be used to effectively curb the sampling complexity and enable real-time control applications. Furthermore, the path integral framework provides a natural way of incorporating existing control architectures as ancillary controllers for shaping the sampling distribution. Our results reveal that even in cases where the ancillary controller would fail, our stochastic control algorithm provides an additional safety and robustness layer. Moreover, in the absence of an existing ancillary controller, our method can be used to train a parametrized importance sampling policy using data from the stochastic rollouts. The algorithm may thereby bootstrap itself by learning an importance sampling policy offline and then refining it to unseen environments during online control. We validate our results on three robotic systems, including hardware experiments on a quadrupedal robot.