Boštjan Potočnik

Time optimal path planning considering acceleration limits

A robot path planning technique is proposed in the paper. It was developed for robots with differential drive, but with minor modifications it could be used for all types of nonholonomic robots. The path was planned in the way to minimise the time of reaching the end point in desired direction and with desired velocity, starting from the initial state described by the start point, initial direction and initial velocity. The limitation was the grip of the tires that results in the acceleration limits. The path is presented as a spline curve and was optimised by placing the control points through which the curve should pass.

Model predictive control systems with discrete inputs

The paper proposes a model predictive control algorithm that can be applied to discrete-time hybrid systems with discrete inputs. The algorithm is based on performance driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a tree of evolution. Nodes of the tree represent reachable state of process, and the branches connect two nodes if a transition exists between the corresponding states. To each node a cost function value is associated and based on this value, the tree exploration is driven. As soon as the tree exploration is finished, the corresponding input is applied to the system and the procedure is repeated.

Model-based Predictive Control of Hybrid Systems: A Probabilistic Neural-network Approach to Real-time Control

This paper proposes an approach for reducing the computational complexity of a model-predictive-control strategy for discrete-time hybrid systems with discrete inputs only. Existing solutions are based on dynamic programming and multi-parametric programming approaches, while the one proposed in this paper is based on a modified version of performance-driven reachability analyses. The algorithm abstracts the behaviour of the hybrid system by building a ’tree of evolution’. The nodes of the tree represent the reachable states of a process, and the branches correspond to input combinations leading to designated states. A cost-function value is associated with each node and based on this value the exploration of the tree is driven. For any initial state, an input sequence is thus obtained, driving the system optimally over a finite horizon. According to the model predictive strategy, only the first input is actually applied to the system. The number of possible discrete input combinations is finite and the feasible set of the states of the system may be partitioned according to the optimization results. In the proposed approach, the partitioning is performed offline and a probabilistic neural network (PNN) is then trained by the set of points at the borders of the state-space partitions. The trained PNN is used as a system-state-based control-law classifier. Thus, the online computational effort is minimized and the control can be implemented in real time.

A New Technique for Translating Discrete Hybrid Automata into Piecewise Affine Systems

The paper proposes a new translation algorithm that translates a hybrid system described as a discrete hybrid automaton (DHA) into an equivalent piecewise affine (PWA) system. The translation algorithm exploits, among others, a new technique for cell enumeration in hyperplane arrangement, all proposed in this paper. The new translation technique enables the transfer of several analysis and synthesis tools developed for PWA systems to a DHA class of hybrid systems.

Path optimisation considering dynamic constraints

Path planning technique is proposed in the paper. It was developed for robots with differential drive, but with minor modification could be used for all types of nonholonomic robots. The path was planned in the way to minimize the time of reaching end point in desired direction and with desired velocity, starting from the initial state described by the start point, initial direction and initial velocity. The constraint was acceleration limit in tangential and radial direction caused by the limited grip of the tires. The path is presented as the spline curve and was optimised by placing the control points trough which the curve should take place.

Optimal path design in robot soccer environment

Path planning technique is proposed in the paper. It was developed for robots with differential drive, but with minor modification could be used for all types of nonholonomic robots. The path was planned in the way to minimize the time of reaching end point in desired direction and with desired velocity, starting from the initial state described by the start point, initial direction and initial velocity. The limitation was the grip of the tires that results in the acceleration limits. The path is presented as the spline curve and was optimised by placing the control points trough which the curve should take place.

Path planning considering acceleration limits

Path planning technique is proposed in the paper. It was developed for robots with different drive, but with minor modification could be used for all types of nonholonomic robots. The path was planned in the way to minimize the time of reaching end point in desired direction and with desired velocity, starting from the initial state described by the start point, initial direction and initial velocity. The limitation was the grip of the tires that results in the acceleration limits. The path is presented as the spline curve and was optimised by placing the control points through which the curve should take place.

Control of discrete time hybrid systems with discrete inputs

The paper proposes a model predictive control approach to the hybrid systems with discrete inputs only. The algorithm, which takes into account a model of a hybrid system described as MLD (mixed logical dynamical) system, is based on performance driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a tree of evolution. Nodes of the tree represent reachable states of a process, and the branches connect two nodes if a transition exists between the corresponding states. To each node a cost function value is associated and based on this value, the tree exploration is driven. As soon as the tree is explored, the corresponding input is applied to the system and the procedure is repeated.

SCHEDULING OF HYBRID SYSTEMS: MULTI PRODUCT BATCH PLANT

Abstract The paper proposes a solution to a class of scheduling problems where the goal is to minimize the schedule (production) time. The algorithm, which takes into account a model of a hybrid system described as MLD ( mixed logical dynamical ) system, is based on performance driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a tree of evolution. Nodes of the tree represent reachable states of a process, and the branches connect two nodes if a transition exists between the corresponding states. To each node a cost function value is associated and based on this value, the tree exploration is driven. As soon as the tree is explored, the global solution to the scheduling problem is obtained.