4,540 research outputs found

    Hybrid Probabilistic Trajectory Optimization Using Null-Space Exploration

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    In the context of learning from demonstration, human examples are usually imitated in either Cartesian or joint space. However, this treatment might result in undesired movement trajectories in either space. This is particularly important for motion skills such as striking, which typically imposes motion constraints in both spaces. In order to address this issue, we consider a probabilistic formulation of dynamic movement primitives, and apply it to adapt trajectories in Cartesian and joint spaces simultaneously. The probabilistic treatment allows the robot to capture the variability of multiple demonstrations and facilitates the mixture of trajectory constraints from both spaces. In addition to this proposed hybrid space learning, the robot often needs to consider additional constraints such as motion smoothness and joint limits. On the basis of Jacobian-based inverse kinematics, we propose to exploit robot null-space so as to unify trajectory constraints from Cartesian and joint spaces while satisfying additional constraints. Evaluations of hand-shaking and striking tasks carried out with a humanoid robot demonstrate the applicability of our approach

    Towards Minimal Intervention Control with Competing Constraints

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    As many imitation learning algorithms focus on pure trajectory generation in either Cartesian space or joint space, the problem of considering competing trajectory constraints from both spaces still presents several challenges. In particular, when perturbations are applied to the robot, the underlying controller should take into account the importance of each space for the task execution, and compute the control effort accordingly. However, no such controller formulation exists. In this paper, we provide a minimal intervention control strategy that simultaneously addresses the problems of optimal control and competing constraints between Cartesian and joint spaces. In light of the inconsistency between Cartesian and joint constraints, we exploit the robot null space from an information-theory perspective so as to reduce the corresponding conflict. An optimal solution to the aforementioned controller is derived and furthermore a connection to the classical finite horizon linear quadratic regulator (LQR) is provided. Finally, a writing task in a simulated robot verifies the effectiveness of our approach

    A Non-parametric Skill Representation with Soft Null Space Projectors for Fast Generalization

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    Over the last two decades, the robotics community witnessed the emergence of various motion representations that have been used extensively, particularly in behavorial cloning, to compactly encode and generalize skills. Among these, probabilistic approaches have earned a relevant place, owing to their encoding of variations, correlations and adaptability to new task conditions. Modulating such primitives, however, is often cumbersome due to the need for parameter re-optimization which frequently entails computationally costly operations. In this paper we derive a non-parametric movement primitive formulation that contains a null space projector. We show that such formulation allows for fast and efficient motion generation with computational complexity O(n2) without involving matrix inversions, whose complexity is O(n3). This is achieved by using the null space to track secondary targets, with a precision determined by the training dataset. Using a 2D example associated with time input we show that our non-parametric solution compares favourably with a state-of-the-art parametric approach. For demonstrated skills with high-dimensional inputs we show that it permits on-the-fly adaptation as well

    Online Learning for Ground Trajectory Prediction

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    This paper presents a model based on an hybrid system to numerically simulate the climbing phase of an aircraft. This model is then used within a trajectory prediction tool. Finally, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) optimization algorithm is used to tune five selected parameters, and thus improve the accuracy of the model. Incorporated within a trajectory prediction tool, this model can be used to derive the order of magnitude of the prediction error over time, and thus the domain of validity of the trajectory prediction. A first validation experiment of the proposed model is based on the errors along time for a one-time trajectory prediction at the take off of the flight with respect to the default values of the theoretical BADA model. This experiment, assuming complete information, also shows the limit of the model. A second experiment part presents an on-line trajectory prediction, in which the prediction is continuously updated based on the current aircraft position. This approach raises several issues, for which improvements of the basic model are proposed, and the resulting trajectory prediction tool shows statistically significantly more accurate results than those of the default model.Comment: SESAR 2nd Innovation Days (2012

    An ant system algorithm for automated trajectory planning

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    The paper presents an Ant System based algorithm to optimally plan multi-gravity assist trajectories. The algorithm is designed to solve planning problems in which there is a strong dependency of one decision one all the previously made decisions. In the case of multi-gravity assist trajectories planning, the number of possible paths grows exponentially with the number of planetary encounters. The proposed algorithm avoids scanning all the possible paths and provides good results at a low computational cost. The algorithm builds the solution incrementally, according to Ant System paradigms. Unlike standard ACO, at every planetary encounter, each ant makes a decision based on the information stored in a tabu and feasible list. The approach demonstrated to be competitive, on a number of instances of a real trajectory design problem, against known GA and PSO algorithms

    Automatic MGA trajectory planning with a modified ant colony optimization algorithm

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    This paper assesses the problem of designing multiple gravity assist (MGA) trajectories, including the sequence of planetary encounters. The problem is treated as planning and scheduling of events, such that the original mixed combinatorial-continuous problem is discretised and converted into a purely discrete problem with a finite number of states. We propose the use of a two-dimensional trajectory model in which pairs of celestial bodies are connected by transfer arcs containing one deep-space manoeuvre. A modified Ant Colony Optimisation (ACO) algorithm is then used to look for the optimal solutions. This approach was applied to the design of optimal transfers to Saturn and to Mercury, and a comparison against standard genetic algorithm based optimisers shows its effectiveness
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