On the Construction of Safe Controllable Regions for Affine Systems with Applications to Robotics

This paper studies the problem of constructing in-block controllable (IBC) regions for affine systems. That is, we are concerned with constructing regions in the state space of affine systems such that all the states in the interior of the region are mutually accessible through the region's interior by applying uniformly bounded inputs. We first show that existing results for checking in-block controllability on given polytopic regions cannot be easily extended to address the question of constructing IBC regions. We then explore the geometry of the problem to provide a computationally efficient algorithm for constructing IBC regions. We also prove the soundness of the algorithm. We then use the proposed algorithm to construct safe speed profiles for different robotic systems, including fully-actuated robots, ground robots modeled as unicycles with acceleration limits, and unmanned aerial vehicles (UAVs). Finally, we present several experimental results on UAVs to verify the effectiveness of the proposed algorithm. For instance, we use the proposed algorithm for real-time collision avoidance for UAVs.Comment: 17 pages, 18 figures, under review for publication in Automatic

A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories

The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future

VLSI Design of Trusted Virtual Sensors

This work presents a Very Large Scale Integration (VLSI) design of trusted virtual sensors providing a minimum unitary cost and very good figures of size, speed and power consumption. The sensed variable is estimated by a virtual sensor based on a configurable and programmable PieceWise-Affine hyper-Rectangular (PWAR) model. An algorithm is presented to find the best values of the programmable parameters given a set of (empirical or simulated) input-output data. The VLSI design of the trusted virtual sensor uses the fast authenticated encryption algorithm, AEGIS, to ensure the integrity of the provided virtual measurement and to encrypt it, and a Physical Unclonable Function (PUF) based on a Static Random Access Memory (SRAM) to ensure the integrity of the sensor itself. Implementation results of a prototype designed in a 90-nm Complementary Metal Oxide Semiconductor (CMOS) technology show that the active silicon area of the trusted virtual sensor is 0.86 mm 2 and its power consumption when trusted sensing at 50 MHz is 7.12 mW. The maximum operation frequency is 85 MHz, which allows response times lower than 0.25 μ s. As application example, the designed prototype was programmed to estimate the yaw rate in a vehicle, obtaining root mean square errors lower than 1.1%. Experimental results of the employed PUF show the robustness of the trusted sensing against aging and variations of the operation conditions, namely, temperature and power supply voltage (final value as well as ramp-up time)Ministerio de Economía, Industria y Competitividad TEC2014-57971-RConsejo Superior de Investigaciones Científicas 201750E01

HYBRID CONTROL OF ELECTRIC VEHICLE LATERAL DYNAMICS STABILIZATION

This paper presents a novel method for motion control applied to driver stability system of an electric vehicle with independently driven wheels. By formulating the vehicle dynamics using an approximating the tire-force characteristics into piecewise affine functions, the vehicle dynamics cen be described as a linear hybrid dynamical system to design a hybrid model predictive controller. This controller is expected to make the yaw rate follow the reference ensuring the safety of the car passengers. The vehicle speed is estimated using a multi-sensor data fusion method. Simulation results in Matlab/Simulink have shown that the proposed control scheme takes advantages of electric vehicle and enhances the vehicle stability

Nonlinear analysis of vehicle control actuations based on controlled invariant sets

In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant sets of the steering and braking control systems at various velocities and road conditions. Illustration examples show that, depending on the environments, different vehicle dynamic regions can be reached and stabilized by these controllers. The results can be applied to the theoretical basis of their interventions into the vehicle control system