Using Neural Networks for Motion Planning

1. Using Neural Networks for Motion Planning Iraji & Bagheri Supervisor: Dr. Bagheri

2. Outline • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions Sharif University of Techology

3. Basic Concepts • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Robot navigation is one of the key issue in mobile robotics. • The simplest problem is to find a continuous path from a starting location to a target location. • The path of a robot should be: • Safe (collision-free) • Optimal or close to optimal • Natural: In a complex situation the robot does not get lost and goes far away from its destination. Sharif University of Techology

4. Basic Concepts (cont’d) Decomposition • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Global Approaches Road-Map Retraction Methods Require a preprocessing stage (a graph structure of the connectivity of the robot’s free space) • Local Approaches: Need heuristics, e. g. the estimation of local gradients in a potential field • Randomized Approaches • Genetic Algorithms Sharif University of Techology

5. NN for Motion Planning • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Neural networks are used for path generation in non-stationary environments for real-time planning. • The neurons of the network are arranged in a regularly discretized lattice. • A scalar potential field is formed by repetitively generated waves of neural activity, which originate form the target location. • Classification of the models: • Environment type: • Stationary • Dynamic • Environment representation: • Algebraic • Grid-based Sharif University of Techology

6. NN for Motion Planning (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Configuration space (C): Discretized hypercube in RN where N is number of degrees-Of-Freedom (DOF). • Each discrete position in C is associated with a formal neuron. • Each neuron i is connected to its neighbors within a certain radius, which comprise its neighborhood Si. • Dynamics of networks perform an averaging of the potentials of the local neighboring neurons. • The initial activity potential associated with the target location is distributed through the network field. • Neurons associated with obstacle locations receive a negative value on their external inputs. • Each path step is done in the direction of the neighbor with the maximal value. Sharif University of Techology

7. NN Models • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Resistive Grid: • Each neuron is connected to its 2N closest neighbors, where N is dimensionality of the state space. • Evolution of the ith node: • It is based on a numerical approximation of a solution of the Laplace equation (in 2D): Sharif University of Techology

8. NN Models (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Glasius et al: • Discrete-time Hopfield-type NN, whose dynamics is described by: • Ii encodes the information about the target and obstacle position: • where and . Sharif University of Techology

9. NN Models (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Yang et al: • Continuous-time dynamics, which is derived from the Grossberg’s shunting model: • where ,and . • Some additional efforts for tuning and selection of proper network parameters are required. Sharif University of Techology

10. NN Models (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Chen et al: • Decay rate A>0 may be chosen arbitrarily: • where Di=0 for the obstacles, and Di=1, otherwise. • The external input Ii is positive for the target neuron, and is zero, otherwise. • The connection weights wij=1if network neighborhoods are 4-connected, while if the latter are 8-connected. Sharif University of Techology

11. Dynamic Wave Expansion Neural Network (DWENN) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • DWENN algorithm idea: Organize wave propagation similar to waves in water spreading. Sharif University of Techology

12. DWENN (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • A neuron inherits the activity from a neighbor, which is: • Closer to the target neuron • Is not an obstacle neuron and which belongs to: • Active (i.e. this neighbor has a positive activity value) • Actual (i.e. this neighbor has changed its activity level at the previous time step) wave front. • The activities of all neurons constitute a scalar potential field, in which the minimal positive value is always at the target location. • The robot is globally ‘attracted’ by the target, and starts to move as soon as the first wave front reaches its initial position. Sharif University of Techology

13. DWENN (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Initially, the activity values of all neurons and all connection weights are zero. • Three classes of neurons are distinguished with dynamics given by: • For the target (i=i*(t)): xi(t+1)=1 • For its direct neighbors ( ): • For all other neurons: Sharif University of Techology

14. Network Dynamics • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Connection weights are determined in accordance with • Selective flow of neural activity: • (a) k is not an obstacle. • (b) xk(t)>0. • (c) • (d) if (xi(t)+xi(t-1))>0, then xk(t)<xi(t) must hold. Sharif University of Techology

15. Example Target • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions 2 2 1 2 2 Sharif University of Techology

16. Example (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions 3 3 1 3 3 Sharif University of Techology

17. Example (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions 5 5 4 5 5 4 1 4 5 5 4 5 5 Sharif University of Techology

18. Example (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions 7 7 6 7 7 6 5 6 7 7 6 5 1 5 6 7 7 6 5 6 7 7 6 7 7 Sharif University of Techology

19. Example (cont’d) 9 • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions 9 8 9 9 8 7 8 9 9 8 7 6 7 8 9 9 8 7 6 1 6 7 8 9 9 8 7 6 7 8 9 9 8 7 8 9 9 8 9 9 Sharif University of Techology

20. Network Dynamics (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • Property 1: If in a stationary environment the first wave front reaches neuron i at the time step ta, then this neuron becomes active with value xi(ta)=(2ta-1). • Property 2: If there exists a positive weight wij for neuron i, then this weight indicates the gradient direction in the potential field: • Property 3: The activity level of neuron i is bounded by the doubled number of network iterations n: • Property 4: If an active neuron i has become inactive, then it will stay inactive at the following time step. Indeed, if xi(t-1)>0 and xi(t)=0, then xk(t)<xi(t) is always false, therefore, the condition (d) is also false, and , and, hence, xi(t+1)=0. (propagation of inhibitory wave) Property 5: If an active neuron remains active, then its activity level is increased by one at each time step: • Property 6: If neuron i became active at time ti and neuron j at time tj>ti, then xj(t)>xi(t) for all . Sharif University of Techology

21. Obstacle Avoidance in Dynamic Environments • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • An inactive neuron may initiate the propagation of an inhibitory wave. Sharif University of Techology

22. Comparative Simulation • Closing Gate: Chen DWENN Resistive Grid Glasius Yang Sharif University of Techology

23. Comparative Simulation (cont’d) • Freezing up obstacles: Chen DWENN Resistive Grid Glasius Yang Sharif University of Techology

24. Comparative Simulation (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • In all simulations the network consists of 3600 (60×60) neurons representing a 2D workspace. • The statistical evaluations were based on 500 runs per model. • Dynamics of other models are not fast enough to provide rapid adaptation to the sudden stopping of the obstacles Sharif University of Techology

25. Comparative Simulation • Moving Target Pursuit: Chen DWENN Resistive Grid Glasius Yang Sharif University of Techology

26. Conclusions • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • The resistive grid model has the slowest dynamics. Usually, several local maxima appear when the environment is changing rapidly. • The model by Glasius et al. in complex dynamic scenes is not fast enough to adapt to the changes. Some efforts are also needed to find an appropriate set of the model parameters. • The model by Yang et al. requires a larger number of iterations to converge to a solution. • In the model by Chen et al. the network dynamics and the quality of a generated path, significantly depend on the choice of parameters. The most important model parameters are A (the passive decay rate) and , which defines ‘how much’ activity is transferred between a neuron and its neighbors. Sharif University of Techology

27. Conclusions (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • DWENN model is parameter-free. • In the worst case 2N×5 simple binary operations are needed. • To prevent local minima, the propagation of inhibitory waves is triggered. • In a stationary environment the complexity of the DWENN model does not depend on the dimensionality of C. Sharif University of Techology

28. Conclusions (cont’d) • Basic concepts • NN for Motion Planning • NN Models • DWENN • Comparative Simulation • Conclusions • But, by examining experimental results, it is easy to see that the robot does not select optimal path in DWENN. • It seems that it is because of non-inhibitory behavior of stationary obstacles. • Proposed solution: Emanating some inhibitory wave of from obstacles with respect to target. Non-optimal path Sharif University of Techology

29. Any Question? Sharif University of Techology