很多同學會把路徑規劃(Path Planning)和軌跡規劃（Trajectory Planning）這兩個概念混淆，路徑規劃只是表示了機械臂末端在操作空間中的幾何資訊，比如從工作臺的一端（A點）沿直線移動到另一端（B點）。而軌跡規劃則加上了時間律，比如它要完成的任務是從A點開始到B點結束，中間是以梯形的速度規律來執行的（先以一個加速度a加速運動到一定的速度Vmax，然後再以固定的速度Vmax巡航，最後再以加速度-a減速到0，同時到達B點），經過軌跡規劃後，得到的是操作空間位置和時間的關係式。

（orocos_kinematics_dynamics-master\orocos_kdl\examples\trajectory_example.cpp）

int main(int argc,char* argv[]) {
	using namespace KDL;
	// Create the trajectory:
    // use try/catch to catch any exceptions thrown.
    // NOTE:  exceptions will become obsolete in a future version.
	try {
        // Path_RoundedComposite defines the geometric path along
        // which the robot will move.
		//
		Path_RoundedComposite* path = new Path_RoundedComposite(0.2,0.01,new RotationalInterpolation_SingleAxis());


		path->Add(Frame(Rotation::RPY(M_PI,0,0), Vector(-1,0,0)));
		path->Add(Frame(Rotation::RPY(M_PI/2,0,0), Vector(-0.5,0,0)));
		path->Add(Frame(Rotation::RPY(0,0,0), Vector(0,0,0)));
		path->Add(Frame(Rotation::RPY(0.7,0.7,0.7), Vector(1,1,1)));
		path->Add(Frame(Rotation::RPY(0,0.7,0), Vector(1.5,0.3,0)));
		path->Add(Frame(Rotation::RPY(0.7,0.7,0), Vector(1,1,0)));


		path->Finish();


		VelocityProfile* velpref = new VelocityProfile_Trap(0.5,0.1);
		velpref->SetProfile(0,path->PathLength());  
		Trajectory* traject = new Trajectory_Segment(path, velpref);


		Trajectory_Composite* ctraject = new Trajectory_Composite();
		ctraject->Add(traject);
		ctraject->Add(new Trajectory_Stationary(1.0,Frame(Rotation::RPY(0.7,0.7,0), Vector(1,1,0))));



		// use the trajectory
		double dt=0.1;
		std::ofstream of("./trajectory.dat");
		for (double t=0.0; t <= traject->Duration(); t+= dt) {
			Frame current_pose;
			current_pose = traject->Pos(t);
			for (int i=0;i<4;++i)
				for (int j=0;j<4;++j)
					of << current_pose(i,j) << "\t";
			of << "\n";
			// also velocities and accelerations are available !
			//traject->Vel(t);
			//traject->Acc(t);
		}
		of.close();

		// you can get some meta-info on the path:
		for (int segmentnr=0;  segmentnr < path->GetNrOfSegments(); segmentnr++) {
			double starts,ends;
			Path::IdentifierType pathtype;
			if (segmentnr==0) {
				starts = 0.0;
			} else {
				starts = path->GetLengthToEndOfSegment(segmentnr-1);
			}
			ends = path->GetLengthToEndOfSegment(segmentnr);
			pathtype = path->GetSegment(segmentnr)->getIdentifier();
			std::cout << "segment " << segmentnr << " runs from s="<<starts << " to s=" <<ends;
			switch(pathtype) {
				case Path::ID_CIRCLE:
					std::cout << " circle";
					break;
				case Path::ID_LINE:
					std::cout << " line ";
					break;
				default:
					std::cout << " unknown ";
					break;
			}
			std::cout << std::endl;
		}
        std::cout << " trajectory written to the ./trajectory.dat file " << std::endl;

        delete ctraject;
	} catch(Error& error) {
		std::cout <<"I encountered this error : " << error.Description() << std::endl;
		std::cout << "with the following type " << error.GetType() << std::endl;
	}

}
 

		path->Add(Frame(Rotation::RPY(M_PI,0,0), Vector(-1,0,0)));
		path->Add(Frame(Rotation::RPY(M_PI/2,0,0), Vector(-0.5,0,0)));
		path->Add(Frame(Rotation::RPY(0,0,0), Vector(0,0,0)));
		path->Add(Frame(Rotation::RPY(0.7,0.7,0.7), Vector(1,1,1)));
		path->Add(Frame(Rotation::RPY(0,0.7,0), Vector(1.5,0.3,0)));
		path->Add(Frame(Rotation::RPY(0.7,0.7,0), Vector(1,1,0)));
		path->Finish();
 

		VelocityProfile* velpref = new VelocityProfile_Trap(0.5,0.1);
		velpref->SetProfile(0,path->PathLength());  
		Trajectory* traject = new Trajectory_Segment(path, velpref);

		Trajectory_Composite* ctraject = new Trajectory_Composite();
		ctraject->Add(traject);
		ctraject->Add(new Trajectory_Stationary(1.0,Frame(Rotation::RPY(0.7,0.7,0), Vector(1,1,0))));

		double dt=0.1;
		std::ofstream of("./trajectory.dat");
		for (double t=0.0; t <= traject->Duration(); t+= dt) {
			Frame current_pose;
			current_pose = traject->Pos(t);
			for (int i=0;i<4;++i)
				for (int j=0;j<4;++j)
					of << current_pose(i,j) << "\t";
			of << "\n";
		}
		of.close();

		for (int segmentnr=0;  segmentnr < path->GetNrOfSegments(); segmentnr++) {
			double starts,ends;
			Path::IdentifierType pathtype;
			if (segmentnr==0) {
				starts = 0.0;
			} else {
				starts = path->GetLengthToEndOfSegment(segmentnr-1);
			}
			ends = path->GetLengthToEndOfSegment(segmentnr);
			pathtype = path->GetSegment(segmentnr)->getIdentifier();
			std::cout << "segment " << segmentnr << " runs from s="<<starts << " to s=" <<ends;
			switch(pathtype) {
				case Path::ID_CIRCLE:
					std::cout << " circle";
					break;
				case Path::ID_LINE:
					std::cout << " line ";
					break;
				default:
					std::cout << " unknown ";
					break;
			}
			std::cout << std::endl;
		}
        std::cout << " trajectory written to the ./trajectory.dat file " << std::endl;

下面兩張圖是利用matlab繪出的軌跡曲線和機械臂末端與時間的關係，可以看出在明顯的圓弧過渡。

Path velocity呈明顯的梯形形狀。