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Trajectory optimization is a powerful tool for robot motion planning and control. State-of-the-art general-purpose nonlinear programming solvers are versatile, handle constraints in an effective way and provide a high numerical robustness, but they are slow because they do not fully exploit the optimal control problem structure at hand. Existing structure-exploiting solvers are fast but they often lack techniques to deal with nonlinearity or rely on penalty methods to enforce (equality or inequality) path constraints. This works presents FATROP: a trajectory optimization solver that is fast and benefits from the salient features of general-purpose nonlinear optimization solvers. The speed-up is mainly achieved through the use of a specialized linear solver, based on a Riccati recursion that is generalized to also support stagewise equality constraints. To demonstrate the algorithm's potential, it is benchmarked on a set of robot problems that are challenging from a numerical perspective, including problems with a minimum-time objective and no-collision constraints. The solver is shown to solve problems for trajectory generation of a quadrotor, a robot manipulator and a truck-trailer problem in a few tens of milliseconds. The algorithm's C++-code implementation accompanies this work as open source software, released under the GNU Lesser General Public License (LGPL). This software framework may encourage and enable the robotics community to use trajectory optimization in more challenging applications.

In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with changes in the domain topology, need to be tackled appropriately. The second challenge arises when computational resources and the time for evaluating the model become critical in so-called many query scenarios for parametric problems. For example, these problems occur in optimization, uncertainty quantification (UQ), or automatic control and using highly resolved full-order models (FOMs) may become impractical. To address both types of complexity, we present a novel projection-based model order reduction (MOR) approach for deforming domain problems that takes advantage of the time-continuous space-time formulation. We apply it to two examples that are relevant for engineering or biomedical applications and conduct an error and performance analysis. In both cases, we are able to drastically reduce the computational expense for a model evaluation and, at the same time, to maintain an adequate accuracy level. All in all, this work indicates the effectiveness of the presented MOR approach for deforming domain problems taking advantage of a time-continuous space-time setting.

Thanks to the augmented convenience, safety advantages, and potential commercial value, Intelligent vehicles (IVs) have attracted wide attention throughout the world. Although a few autonomous driving unicorns assert that IVs will be commercially deployable by 2025, their implementation is still restricted to small-scale validation due to various issues, among which precise computation of control commands or trajectories by planning methods remains a prerequisite for IVs. This paper aims to review state-of-the-art planning methods, including pipeline planning and end-to-end planning methods. In terms of pipeline methods, a survey of selecting algorithms is provided along with a discussion of the expansion and optimization mechanisms, whereas in end-to-end methods, the training approaches and verification scenarios of driving tasks are points of concern. Experimental platforms are reviewed to facilitate readers in selecting suitable training and validation methods. Finally, the current challenges and future directions are discussed. The side-by-side comparison presented in this survey not only helps to gain insights into the strengths and limitations of the reviewed methods but also assists with system-level design choices.

Generating natural and physically feasible motions for legged robots has been a challenging problem due to its complex dynamics. In this work, we introduce a novel learning-based framework of autoregressive motion planner (ARMP) for quadruped locomotion and navigation. Our method can generate motion plans with an arbitrary length in an autoregressive fashion, unlike most offline trajectory optimization algorithms for a fixed trajectory length. To this end, we first construct the motion library by solving a dense set of trajectory optimization problems for diverse scenarios and parameter settings. Then we learn the motion manifold from the dataset in a supervised learning fashion. We show that the proposed ARMP can generate physically plausible motions for various tasks and situations. We also showcase that our method can be successfully integrated with the recent robot navigation frameworks as a low-level controller and unleash the full capability of legged robots for complex indoor navigation.

Learning various motor skills for quadrupedal robots is a challenging problem that requires careful design of task-specific mathematical models or reward descriptions. In this work, we propose to learn a single capable policy using deep reinforcement learning by imitating a large number of reference motions, including walking, turning, pacing, jumping, sitting, and lying. On top of the existing motion imitation framework, we first carefully design the observation space, the action space, and the reward function to improve the scalability of the learning as well as the robustness of the final policy. In addition, we adopt a novel adaptive motion sampling (AMS) method, which maintains a balance between successful and unsuccessful behaviors. This technique allows the learning algorithm to focus on challenging motor skills and avoid catastrophic forgetting. We demonstrate that the learned policy can exhibit diverse behaviors in simulation by successfully tracking both the training dataset and out-of-distribution trajectories. We also validate the importance of the proposed learning formulation and the adaptive motion sampling scheme by conducting experiments.

Motion planning methods like navigation functions and harmonic potential fields provide (almost) global convergence and are suitable for obstacle avoidance in dynamically changing environments due to their reactive nature. A common assumption in the control design is that the robot operates in a disjoint star world, i.e. all obstacles are strictly starshaped and mutually disjoint. However, in real-life scenarios obstacles may intersect due to expanded obstacle regions corresponding to robot radius or safety margins. To broaden the applicability of aforementioned reactive motion planning methods, we propose a method to reshape a workspace of intersecting obstacles into a disjoint star world. The algorithm is based on two novel concepts presented here, namely admissible kernel and starshaped hull with specified kernel, which are closely related to the notion of starshaped hull. The utilization of the proposed method is illustrated with examples of a robot operating in a 2D workspace using a harmonic potential field approach in combination with the developed algorithm.

Chemists need to perform many laborious and time-consuming experiments in the lab to discover and understand the properties of new materials. To support and accelerate this process, we propose a robot framework for manipulation that autonomously performs chemistry experiments. Our framework receives high-level abstract descriptions of chemistry experiments, perceives the lab workspace, and autonomously plans multi-step actions and motions. The robot interacts with a wide range of lab equipment and executes the generated plans. A key component of our method is constrained task and motion planning using PDDLStream solvers. Preventing collisions and spillage is done by introducing a constrained motion planner. Our planning framework can conduct different experiments employing implemented actions and lab tools. We demonstrate the utility of our framework on pouring skills for various materials and two fundamental chemical experiments for materials synthesis: solubility and recrystallization.

In this paper, a sampling-based trajectory planning algorithm for a laboratory-scale 3D gantry crane in an environment with static obstacles and subject to bounds on the velocity and acceleration of the gantry crane system is presented. The focus is on developing a fast motion planning algorithm for differentially flat systems, where intermediate results can be stored and reused for further tasks, such as replanning. The proposed approach is based on the informed optimal rapidly exploring random tree algorithm (informed RRT*), which is utilized to build trajectory trees that are reused for replanning when the start and/or target states change. In contrast to state-of-the-art approaches, the proposed motion planning algorithm incorporates a linear quadratic minimum time (LQTM) local planner. Thus, dynamic properties such as time optimality and the smoothness of the trajectory are directly considered in the proposed algorithm. Moreover, by integrating the branch-and-bound method to perform the pruning process on the trajectory tree, the proposed algorithm can eliminate points in the tree that do not contribute to finding better solutions. This helps to curb memory consumption and reduce the computational complexity during motion (re)planning. Simulation results for a validated mathematical model of a 3D gantry crane show the feasibility of the proposed approach.

This study proposes a safe and sample-efficient reinforcement learning (RL) framework to address two major challenges in developing applicable RL algorithms: satisfying safety constraints and efficiently learning with limited samples. To guarantee safety in real-world complex environments, we use the safe set algorithm (SSA) to monitor and modify the nominal controls, and evaluate SSA+RL in a clustered dynamic environment which is challenging to be solved by existing RL algorithms. However, the SSA+RL framework is usually not sample-efficient especially in reward-sparse environments, which has not been addressed in previous safe RL works. To improve the learning efficiency, we propose three techniques: (1) avoiding behaving overly conservative by adapting the SSA; (2) encouraging safe exploration using random network distillation with safety constraints; (3) improving policy convergence by treating SSA as expert demonstrations and directly learn from that. The experimental results show that our framework can achieve better safety performance compare to other safe RL methods during training and solve the task with substantially fewer episodes. Project website: //hychen-naza.github.io/projects/Safe_RL/.

Reinforcement Learning (RL) has seen many recent successes for quadruped robot control. The imitation of reference motions provides a simple and powerful prior for guiding solutions towards desired solutions without the need for meticulous reward design. While much work uses motion capture data or hand-crafted trajectories as the reference motion, relatively little work has explored the use of reference motions coming from model-based trajectory optimization. In this work, we investigate several design considerations that arise with such a framework, as demonstrated through four dynamic behaviours: trot, front hop, 180 backflip, and biped stepping. These are trained in simulation and transferred to a physical Solo 8 quadruped robot without further adaptation. In particular, we explore the space of feed-forward designs afforded by the trajectory optimizer to understand its impact on RL learning efficiency and sim-to-real transfer. These findings contribute to the long standing goal of producing robot controllers that combine the interpretability and precision of model-based optimization with the robustness that model-free RL-based controllers offer.