Kinodynamic RRT planners are considered to be general tools for effectively finding feasible trajectories for highdimensional 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.

Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate random states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.

This paper proposes the use of a randomized kinodynamic planning technique to synthesize dynamic motions for cable-suspended parallel robots. Given two mechanical states of the robot, both with a prescribed position and velocity, the method attempts to connect them by a collision-free trajectory that respects the joint and force limits of the actuators, keeps the cables in tension, and takes the robot dynamics into account. The method is based on the construction of a bidirectional rapidly-exploring random tree over the state space. Remarkably, the technique can be used to cross forward singularities of the robot in a predictable manner, which extends the motion capabilities beyond those demonstrated in previous work. The paper describes experiments that show the performance of the method in point-topoint operations with specific cable-driven robots, but the overall strategy remains applicable to other mechanism designs.

Forward singularities, also known as direct, or actuator singularities, cause many problems to the planning and control of robot motions. They yield position errors and rigidity losses of the robot, and generate unbounded actions in typical control laws. To circumvent these issues, this paper proposes a randomized kinodynamic planner for computing trajectories avoiding such singularities. Given initial and final states for the robot, the planner attempts to connect them by means of a dynamically-feasible, singularity-free trajectory that also respects the force limits of the actuators. The performance of the strategy is illustrated in simulation by means of a parallel robot performing a highlydynamic task.

Parallel robots exhibit the so-called forward singularities, which complicate substantially the planning and control of their motions. Often, such complications are circumvented by restricting the motions to singularity-free regions of the workspace. However, this comes at the expense of reducing the motion range of the robot substantially. It is for this reason that, recently, efforts are underway to control singularitycrossing trajectories. This paper proposes a reliable controller to stabilize such kind of trajectories. The controller is based on the classical theory of linear quadratic regulators, which we adapt appropriately to the case of parallel robots. As opposed to traditional computed-torque methods, the obtained controller does not rely on expensive inverse dynamics computations. Instead, it uses an optimal control law that is easy to evaluate, and does not generate instabilities at forward singularities. The performance of the controller is exemplified on a five-bar parallel robot accomplishing two tasks that require the traversal of singularities.