Fast robotic pick-and-place with suction cups is a crucial component in the current development of automation in logistics (factory lines, e-commerce, etc.) By "critically fast" we mean the fastest possible movements for transporting an object such that it does not slip or fall from the suction cup. The main difficulties are: (i) handling the contact between the suction cup and the object, which fundamentally involves kinodynamic constraints, and (ii) doing so at a low computational cost, typically a few hundreds of milliseconds. To address these difficulties, we propose (a) a model for suction cup contacts, (b) a procedure to identify the contact stability constraint based on that model, and (c) a procedure to parameterize, in a time-optimal manner, arbitrary geometric paths under the identified contact stability constraint. We experimentally validate the proposed pipeline on a physical robot system: the cycle time for a typical pick-and-place task was less than 5 seconds, planning and execution times included. The full pipeline is released as open-source for the robotics community.
This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an ini ial configuration and velocity to a goal configuration and velocity while obeying physically based dynamical models and avoiding obstacles in the robot’s environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot’s high-dimensional configuration space. Kinodynamic planning is treated as a motion-planning problem in a higher dimensional state space that has both first-order differential constraints and obstacle-based global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized path-planning techniques do not directly apply to planning trajectories in the state space. The authors have developed a randomized planning approach that is particularly tailored to trajectory plannin... In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization. CHOMP uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component. CHOMP can be used to locally optimize feasible trajectories, as well as to solve motion planning queries, converging to low-cost trajectories even when initialized with infeasible ones. It uses Hamiltonian Monte Carlo to alleviate the problem of convergence to high-cost local minima (and for probabilistic completeness), and is capable of respecting hard constraints along the trajectory. We present extensive experiments with CHOMP on manipulation and locomotion tasks, using seven-degree-of-freedom manipulators and a rough-terrain quadruped robot. Finding the time-optimal parameterization of a given path subject to kinodynamic constraints is an essential component in many robotic theories and applications. The objective of this paper is to provide a general, fast, and robust implementation of this component. For this, we give a complete solution to the issue of dynamic singularities, which are the main cause of failure in existing implementations. We then present an open-source implementation of the algorithm in C++ Python and demonstrate its robustness and speed in various robotics settings. Time-optimal path parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: numerical integration (NI) and convex optimization (CO). The NI-based methods are fast but difficult to implement and suffer from robustness issues, while CO-based approaches are more robust but, at the same time, significantly slower. Here, we propose a new approach to TOPP based on reachability analysis. The key insight is to recursively compute reachable and controllable sets at discretized positions on the path by solving small linear programs. The resulting algorithm is faster than NI-based methods and as robust as CO-based ones (100 success rate), as confirmed by extensive numerical evaluations. Moreover, the proposed approach offers unique additional benefits: admissible velocity propagation and robustness to parametric uncertainty can be derived from it in a simple and natural way. We present a novel approach to solving the trajectory plan ning problem (TPP) in time-varying environments. The es sence of our approach lies in a heuristic but natural decom position of TPP into two subproblems: (1) planning a path to avoid collision with static obstacles and (2) planning the velocity along the path to avoid collision with moving obsta cles. We call thefirst subproblem the path planning problem (PPP) and the second the velocity planning problem (VPP). Thus, our decomposition is summarized by the equation TPP => PPP + VPP. The symbol => indicates that the de composition holds under certain assumptions, e.g., when obstacles are moving independently of (i.e., not tracking ) the robot. Furthermore, we pose the VPP in path-time space, where time is explicitly represented as an extra dimension, and reduce it to a graph search in this space. In fact, VPP is transformed to a two-dimensional PPP in path-time space with some additional constraints. Algorithms are then pre sented to solve the VPP w... The minimum-time manipulator control problem is solved for the case when the path is specified and the actuator torque limitations are known. The optimal open-loop torques are found, and a method is given for implementing these torques with a conventional linear feedback control system. The algorithm allows bounds on the torques that may be arbitrary functions of the joint angles and angular velocities. This method is valid for any path and orientation of the end- effector that is specified. The algorithm can be used for any manipulator that has rigid links, known dynamic equations of motion, and joint angles that can be determined at a given position on the path. This paper focuses on time-optimal path-constrained trajectory planning, a subproblem in time-optimal motion plan- ning of robot systems. Through a nonlinear change of variables, the time-optimal trajectory planning is transformed here into a convex optimal control problem with a single state. Various convexity-preserving extensions are introduced, resulting in a versatile approach for optimal trajectory planning. A direct tran- scription method is presented that reduces finding the globally optimal trajectory to solving a second-order cone program using robust numerical algorithms that are freely available. Validation against known examples and application to a more complex example illustrate the versatility and practicality of the new method. Kinodynamic RRT planners are considered to be general tools for effectively finding feasible trajectories for high-dimensional dynamical systems. However, they struggle when holonomic constraints are present in the system, such as those arising in parallel manipulators, in robots that cooperate to fulfill a given task, or in situations involving contacts with the environment. In such cases, the state space becomes an implicitly-defined manifold, which makes the diffusion heuristic inefficient and leads to inaccurate dynamical simulations. To address these issues, this paper presents an extension of the kinodynamic RRT planner that constructs an atlas of the state-space manifold incrementally, and uses this atlas both to generate random states and to dynamically steer the system towards such states. To the best of our knowledge, this is the first randomized kinodynamic planner that explicitly takes holonomic constraints into account. We validate the approach in significantly-complex systems. This paper presents a method for generating dynamically feasible, keyframe-interpolating motions for robots undergoing contact, such as in legged locomotion and manipulation. The first stage generates a twice-differentiable interpolating path that obeys kinematic contact constraints up to a user-specified tolerance. The second stage optimizes speeds along the path to minimize time while satisfying dynamic constraints. The method supports velocity, acceleration, and torque constraints, and polyhedral contact friction constraints at an arbitrary number of contact points. The method is numerically stable, and empirical running time is weakly linear in the number of degrees of freedom and polynomial in the time-domain grid resolution. Experiments demonstrate that full-body motions for robots with 100 degrees of freedom and dozens of contact points are calculated in seconds.