Trajectory Prediction for Moving Objects Using Artificial Neural Networks

Pierre Payeur, Hoang Le-Huy, Clement M.

Human Factors: The Journal of the Human Factors and Ergonomics Society

Summary

                  Prediction of objects trajectory and position is very important for industrial robots and servo systems, where this kind of information might be used for control, capture and other observation issues.

Parts’ trajectories are often unknown and catching object problem can be useful for example in a typical loading/unloading problem of a robot grasping an object (for instance s box) from a slide or a conveyor.

In such a condition of course accuracy is strictly important, both for achieving the goal and for safety purposes.

An optimum off-line method is path planning based on cubit polynomials with dynamics added (G. Sahar, Hollerbach, 1986), but this method involved a lot of computation and it is done off-line, being not flexible.

The authors propose the use of Artificial Neural Networks (ANN), which can be computed faster and most of all can learn the system, being adaptable and flexible. The problem can be defined as the prediction of the trajectory of a moving object in real time, with minimum error, with no collision on an arbitrary path.

·       Model

Time t₀ is defined as the time in which the manipulator starts moving, the prediction is done with the period of time T. The trajectory model is defined with a cubic function: χ(t)=1/6α₀t³+1/2β₀t²+γ₀t+χ₀, where χ represents the position, orientation, velocity or acceleration according on needs.

Neural network are trained to define the values of the coefficients α₀, β₀, γ₀ at each change of trajectory for which they have to be recalculated, the presence of pre- and post-conditioning allows the need of a long network so that in the end there are 3 inputs, two layers of 20 hidden cells each and one output cell.

The global predictive structure is a multiplication of this basic topology by the number of d.o.f. .The Network is modeled so that it basically obtains information about the change in position and not the exact position, this method ensures reduction of calculations, but pre and post conditioning are then of course required in order to ensure the start and continuation of the calculations. Sampling period T too many times also should be avoided, so the preconditioning module computes differences between the known positions and feeds the network is pseudo-displacement value, so the network will process it and generates the anticipated pseudo-variation of the position or orientation, the post-conditioning module finds then velocity and acceleration through kinematics. The processed data from the neural nets is normalized so that the maximum value is lower than the activation function maxima (in this case a bipolar sigmoidal activation function with a range from -1.0 to 1.0). Between two successive sampling there is a maximum coordinate variation ∆p_max, while limitation in resolution is the minimum detection possible (∆p_resolution), so that the number of possible steps to consider is S_Tsingle=2∆p_max/∆p_resolution+1, which must be globally should be powered by three for each of the inputs. The size of the data can be reduced since two successive position or orientation variation are always of a similar amplitude with a constant sampling rate, so it can be assumed hat there is a maximum difference, tables (Appendix C) help for calculations shown at page 151. Once the input triplet is processed with the cubic model already introduced (to ensure that the output data presented to the network are exact), these are normalized between ±0.8 to avoid extremes, at that point the back-propagation algorithm and the pseudo-random presentation order are used for training the data (triplets are not presented in a fixed order, but the entire set must be used within one epoch).

Key Concepts

Artificial Neural Network, Path Planning, Trajectory Prediction

Conclusion

The method appear to be optimal and working as the polynomial trajectory model but being more flexible. Anticipated values are also more reliable and variances are more similar between axis so that errors could be improved and controlled.