The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.

SUMMARYThis paper presents a method of planning a sub-optimal trajectory for a mobile manipulator subject to mechanical and control constraints. The path of the end-effector is defined as a curve that can be parameterised by any scaling parameter—the reference trajectory of a mobile platform is not needed. Constraints connected with the existence of mechanical limits for a given manipulator configuration, collision avoidance conditions and control constraints are considered. Nonholonomic constraints in a Pfaffian form are explicitly incorporated to the control algorithm. To avoid manipulator singularities, the motion of the robot is planned in order to maximise the manipulability measure.

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The aim of this study was to develop a physical activity advisory system supporting the correct implementation of sport exercises using inertial sensors and machine learning algorithms. Specifically, three mobile sensors (tags), six stationary anchors and a system-controlling server (gateway) were employed for 15 scenarios of the series of subsequent activities, namely squats, pull-ups and dips. The proposed solution consists of two modules: an activity recognition module (ARM) and a repetition-counting module (RCM). The former is responsible for extracting the series of subsequent activities (so-called scenario), and the latter determines the number of repetitions of a given activity in a single series. Data used in this study contained 488 three defined sport activity occurrences. Data processing was conducted to enhance performance, including an overlapping and non-overlapping window, raw and normalized data, a convolutional neural network (CNN) with an additional post-processing block (PPB) and repetition counting. The developed system achieved satisfactory accuracy: CNN + PPB: non-overlapping window and raw data, 0.88; non-overlapping window and normalized data, 0.78; overlapping window and raw data, 0.92; overlapping window and normalized data, 0.87. For repetition counting, the achieved accuracies were 0.93 and 0.97 within an error of ±1 and ±2 repetitions, respectively. The archived results indicate that the proposed system could be a helpful tool to support the correct implementation of sport exercises and could be successfully implemented in further work in the form of web application detecting the user’s sport activity.