In the paper we present the module which uses triangle mesh of the robot to detect collisions between parts of the robot. To this end, the triangle to triangle intersection test is applied. To speed up the computation the bounding box test is carried out at the beginning. We show the properties and performance of the collision detection module. Then, we propose the method which uses Gaussian mixture to determine self- collision model. The method is significantly faster than the method which uses triangle meshes but less precise. The collision detection methods can be applied during motion planning as well as during execution of the planned motion to detect infeasible configurations of the robot.

 We present a new motion planning method for a biped robot. The method uses elevation map of the environment to plan the path of the feet and robot's body on rough terrain. We show how to incorporate modules which determine footholds, posture of the robot and check if the planned path is secure into a single general framework based on the Rapidly-exploring Random Trees. We describe the controller which stabilizes the robot during execution of the planned path. In the paper the implementation of the method for the Atlas robot in Gazebo environment is presented.

 Predicting the motions of rigid objects under contacts is a necessary precursor to planning of robot manipulation of objects. We show how to bring together the advantages of learning approaches and kinematic optimization to achieve learned simulators of specific objects that outperform previous learning approaches. Our approach employs a fast simplified collision checker and a learning method. The learner predicts trajectories for the object. These are optimised post prediction to minimise interpenetrations according to the collision checker. In addition we show that cleaning the training data prior to learning can also improve performance.

 Outdoor experiment: Achieving full autonomy in a mobile robot requires combining robust environment perception with on-board sensors, efficient environment mapping, and real-time motion planning. All these tasks become more challenging when we consider a natural, outdoor environment and a robot that has many degrees of freedom (d.o.f.). In this paper we address the issues of motion planning in a legged robot walking over a rough terrain, using only its on-board sensors to gather the necessary environment model. The proposed solution takes the limited perceptual capabilities of the robot into account. A~multi-sensor system is considered for environment perception. The key idea of the motion planner is to use the dual representation concept of the map: (i) a higher-level planner applies the A* algorithm for coarse path planning on a low-resolution elevation grid, and (ii) a lower-level planner applies the guided-RRT (Rapidly-exploring Random Tree) algorithm to find a sequence of feasible motions on a more precise but smaller map. This paper contributes a new method that can learn the terrain traversability cost function to the benefit of the A* algorithm. A probabilistic regression technique is applied for the traversability assessment with the typical RRT-based motion planner used to explore the space of traversability values. The efficiency of our motion planning approach is demonstrated in simulations that provide ground truth data unavailable in field tests. However, the simulation-verified approach is then thoroughly tested under real-world conditions in experiments with two six-legged walking robots having different perception systems.

In this paper we present a traversability assessment method for motion planning in autonomous walking robots. The aim is to plan the motion of the robot in a real scenario on a rough terrain, where the level of details in the obtained terrain maps is not sufficient for motion planning. A guided RRT (Rapidly-exploring Random Trees)  algorithm is used to plan the motion of the robot on rough terrain. We are looking for a method that can learn the terrain traversability cost function to the benefit of the guiding function of the planning algorithm. A probabilistic regression technique is used to solve the traversability assessment problem.