This is a correction to [Duindam and Stramigioli, “Singularity-free dynamic equations of open-chain mechanisms with general holonomic and nonholonomic joints,” IEEE Trans. Robot., vol. 24, no. 3, pp. 527-526, Jun. 2008] where the singularity-free dynamic equations of mechanical systems with Euclidean or non-Euclidean configuration spaces are presented. We present the correct explicit expressions of the equations presented in the above referenced paper.

Robotic manipulators on ships and platforms suffer from large inertial forces due to the non-inertial motion of the ship or platform. When operating in high sea state, operation of such manipulators can be made more efficient and robust if these non-inertial effects are taken into account in the motion planning and control systems. Motivated by this application, we present a rigorous and singularity-free formulation of the dynamics of a robotic manipulator mounted on a non-inertial base. We extend the classical dynamics equations for a serial manipulator to include the 6-DoF motion of the non-inertial base. Then, we show two examples of a 1-DoF and a 4-DoF manipulator to illustrate how these non-inertial effects can be taken into account in the motion planning.

The large number of degrees of freedom in legged robots give rise to complicated dynamics equations. Analyzing these equations or using them for control can therefore be a difficult and non-intuitive task. A simplification of the complex multi-body dynamics can be achieved by instantaneously reducing it to an equivalent single inertial entity called the locked inertia or the composite rigid body inertia.

This paper addresses the use of robotic tissue manipulation in medical needle insertion procedures to improve targeting accuracy and to help avoid damaging sensitive tissues. To control these multiple, potentially competing objectives, we present a phased controller that operates one manipulator at a time using closed-loop imaging feedback. We present an automated procedure planning technique that uses tissue geometry to select the needle insertion location, manipulation locations, and controller parameters. The planner uses a stochastic optimization of a cost function that includes tissue stress and robustness to disturbances. We demonstrate the system on 2D tissues simulated with a mass-spring model, including a simulation of a prostate brachytherapy procedure. It can reduce targeting errors from more than 2 cm to less than 1 mm, and can also shift obstacles by over 1 cm to clear them away from the needle path.

Accurate insertion of needles to targets in 3D anatomy is required for numerous medical procedures. To reduce patient trauma, a "fireworks" needle insertion approach can be used in which multiple needles are inserted from a single small region on the patient's skin to multiple targets in the tissue. In this paper, we explore motion planning for "fireworks" needle insertion in 3D environments by developing an algorithm based on Rapidly-exploring Random Trees (RRTs). Given a set of targets, we propose an algorithm to quickly explore the configuration space by building a forest of RRTs and to find feasible plans for multiple steerable needles from a single entry region. We present two path selection algorithms with different optimality considerations to optimize the final plan among all feasible outputs. Finally, we demonstrate the performance of the proposed algorithm with a simulation based on a prostate cancer treatment environment.

Bevel-tip flexible needles have greater mobility than straight rigid needles, and can be used to reach targets behind sensitive or impenetrable areas. Accurately planning and executing the optimal motions for such steerable needles is difficult, however, and requires solving inverse kinematics for a nonholonomic system.This paper presents an approach to 3D motion planning for bevel-tip needles in an environment with obstacles. Instead of discretizing the configuration space as in earlier work, we discretize the control space, such that the trajectory of the needle can be expressed analytically without the need for approximate numerical simulation. This results in a fast optimization routine that finds a locally optimal path in a 3D environment with obstacles, requiring just a few seconds of computation time on a standard PC.We introduce two different discretization strategies that lead to differently structured paths and show that both produce valid trajectories from start to goal. To our knowledge, the presented method is the first to address motion planning for bevel-tip needles in a 3D environment with obstacles.

Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to Ropfn. This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example, in the case of ball joints or a free-floating mechanism. This paper discusses an extension of classical methods that allows for a more general class of joints, including all joints with a Lie group structure as well as nonholonomic joints. The model equations are derived using the Boltzmann-Hamel equations and have very similar structure and complexity as obtained using classical methods. However, singularities are avoided through the use of global non-Euclidean configuration coordinates, together with mappings describing a local Euclidean structure around each configuration. The resulting equations are explicit (unconstrained) differential equations, both for holonomic and nonholonomic joints, which do not require a coordinate atlas and can be directly implemented in simulation software.

One of the potential benefits of robotic systems in cardiac surgery is that their use can increase the number of possible off-pump (beating heart) coronary artery bypass grafting procedures. Robotic systems can actively synchronize the motion of surgical tools to the motion of the surface of the heart, with the surgeon specifying only the relative motion of the tool with respect to the heart. Accurate prediction of the motion of the heart surface is obviously of crucial importance for the safety and robustness of such a system. This paper presents a novel approach to predict the motion of the surface of a beating heart. We show how ECG and respiratory information can be used to extract two periodic components from the quasi-periodic motion of the heart surface. Contrary to most existing literature, we consider the full geometric motion, including rotation due to respiration. We then show how to combine the periodic components to accurately predict future motion of the heart surface, and how this information can be used to design an explicit controller that asymptotically stabilizes the relative motion of the surgical tool to a desired relative distance and orientation.

Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to R". This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example in the case of ball joints or a free-floating mechanism. This paper discusses an extension of classical methods to allow for a very general class of joints, including all joints with a Lie group structure as well as nonholonomic joints. The model equations are derived using the Boltzmann-Hamel equations and have very similar structure and complexity as obtained using classical methods, but they do not suffer from singularities. Furthermore, the equations are explicit differential equations (both for holonomic and nonholonomic joints) and can be directly implemented in simulation software.

Research on nonholonomic mechanical systems has focused mainly on describing geometric structure, controllability, and motion planning, yet little attention has been paid to several energy aspects of these systems. This paper describes a method to model nonholonomic mechanical systems as reduced-order port-controlled Hamiltonian systems, in which the energy structure is shown explicitly. We show how very simple equations are obtained for the example of the snakeboard, and then discuss how these equations can be used to derive an energy-based controller in an intuitive way.

In this paper, we derive a coordinate-free formulation of a passive controller that makes a mechanical system track reference curves in a potential field. Contrary to conventional reference tracking, we do not specify a single time-varying trajectory that the system has to track. Instead, we specify a whole curve that the system has to stay on at all times. Using tools from differential geometry, we first derive a controller that makes the system move along arbitrary (smooth enough) reference curves while keeping the kinetic energy constant. We then apply the results to the case of movement in an artificial potential field, in which case, the reference curves are completely determined by the potential field and cannot be chosen arbitrarily. Simulation then shows the performance of the controller on a benchmark robot with two degrees of freedom.

In this paper, we discuss the modeling of the kinematics and dynamics of compliant contact between bodies moving in Euclidean space. First, we derive the kinematic equations describing the motion of the contact point when two rigid bodies are rolling on each other. Secondly, we extend these results to describe the motion of the closest points between two rigid bodies moving freely in space. Then, we use these results to model compliant contact between bodies, using a spatial spring and a damper to model energy stored and dissipated during contact.

Considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for an experimental planar robotic fish system that is propelled using carangiform-like locomotion. Our model for the fish's propulsion is based on quasi-steady fluid flow. Using this model, we propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment.

This article presents a passive way to implement varying spatial springs. These are springs with controlling ports which can be used to modify their spatial rest length or spatial properties. These controlling ports have a dual structure which allows one to supervise the potential energy injected into the spring by varying its properties. A direct application in tele-manipulation using geometric scattering is briefly described.